Research on the Dissipative Evolution of the Regional Digital Innovation Ecosystem from the Perspective of Symbiosis Theory

Abstract

Constructing the regional digital innovation ecosystem is not merely a strategic response to the global digital transformation but also an essential driver for fostering high-quality regional development. From the perspective of symbiosis and in combination with the theory of dissipative structure, and the evaluation index system of “digital innovation investment – digital innovation environment ” framework is constructed. Then, the evolution of the regional digital innovation ecosystem, characterized by dissipative processes, is analyzed using the “global entropy–catastrophe progression” evaluation model. Through empirical analysis of the dissipative evolution of digital innovation ecosystems across 30 Chinese provinces between 2013 and 2023, this study revealed that: (1) In the sample areas, the digital innovation ecosystem’s dynamic evolution meets the conditions required for forming a dissipative structure. (2) The level of digital innovation dissipation in the sample areas has generally shown an upward trend year by year. Still, no dissipation structure was formed during the research period. (3) There is an evolutionary trajectory from the third quadrant to the second quadrant and finally to the first quadrant is often shown by the two-dimensional framework of a “digital innovation investment-digital innovation environment” in the sample areas. Both the digital innovation environment and investment evaluation values exhibit an increased tendency. The results play a key role in strengthening China’s digital innovation ecosystem and promoting long-term social development.

1. Introduction

Innovative development has entered the digital age as a result of the global digital economy’s rapid growth [1]. The fundamental transformation process driven by digital technology, which strategically harnesses its essential resources and capabilities to produce value for stakeholders, has led to significant improvements and innovations across all sectors of society [2,3]. This change has strengthened the regional innovation ecosystem’s value creation and capture processes while also endowing it with specific digital traits [3]. Accordingly, it is possible to view the regional digital innovation ecosystem (Hereinafter referred to as the RDIES system) as a digital extension of the innovation ecosystem hypothesis. Amid global economic recovery and innovation catch-up, RDIES systems have emerged as a vital strategic choice for countries seeking innovation leadership [4]. As a driver of regional innovation and economic growth, it supports high-quality development and exerts a growing influence globally. However, issues like low efficiency, uncoordinated development, and a lack of overall innovation continue to plague China’s RDIES system [5]. These issues make it difficult for digital innovation entities to interact and cooperate as well as to integrate and share resources. To a certain extent, this hinders the in-depth implementation of the Digital China strategy. Furthermore, the development and functioning within China’s RDIES systems are severely hampered by the current trend of anti-globalization and the escalation of worldwide geopolitical tensions [6]. One of the main challenges currently facing RDIES systems is achieving the efficient integration and deployment of digital innovation elements under conditions of globalization and digitalization, encouraging the transition of these elements from simple assembly to organic collaboration, and facilitating effective cross-border, cross-industry, and cross-space collaboration among digital innovation entities, thereby increasing the efficiency of digital innovation achievement transformation.

A complex and dynamic system inside a particular geographic area, the RDIES system is where digital innovation actors collaborate effectively across borders and spaces using digital innovation platforms [7]. Compared to traditional regional innovation ecosystems, this system is characterized by greater heterogeneity among participating entities and a more pronounced driving effect on innovation and development [8]. Currently, research on the RDIES system has attracted increasing scholarly attention. The major themes include defining the connotation of the ecosystem [9,10], identifying its constituent elements [11], exploring value co-creation [12,13], analyzing the evolution mechanism [14], and examining governance mechanisms [15]. From a measurement and assessment standpoint, the main focus is on the resilience measurement and resilience enhancement of RDIES systems [7,16], health evaluation [4,17], symbiosis degree evaluation [1,18], niche suitability [19,20], energy level measurement and energy level enhancement [21], and so on. The influence of components like digital technology, digital innovation environments, and digital innovation entities should be the main focus from the standpoint of influencing variables [17]. Overall, research on the RDIES system has attracted considerable attention worldwide. However, several limitations remain. First, as a cross-disciplinary research subject that spans economics, sociology, geography, and other fields, the RDIES system has not yet been sufficiently examined through an integrated interdisciplinary perspective. Specifically, research combining ecological and complexity science frameworks with the study of these ecosystems is still scarce, limiting the ability to fully grasp their inherent complexity. Second, existing studies have primarily concentrated on the basic concepts, structural dimensions, measurement, and evaluation of RDIES systems. Most of this work adopts a static perspective, often neglecting the dynamic characteristics of the systems. Consequently, little attention has been paid to the interplay between internal and external factors, and it remains challenging to reveal, from a macro-level perspective, the dynamic processes through which RDIES systems achieve complex adaptability via material and energy exchange under the influence of external environments. As a result, the deeper evolutionary patterns of these ecosystems are difficult to discern.

Examining regional digital innovation activities through a symbiotic lens reveals the interconnections among digital innovation entities and their coordination with non-biological components. The RDIES system is, first, a dynamic and complex system composed of multiple symbiotic units [1], which interact and collaborate via digital innovation platforms, adapting to and influencing their symbiotic environment. Second, this perspective highlights not only the interactions among units but also the role of resource flows, energy exchange, and evolving relationships in shaping the system. Integrating symbiosis theory with in-depth research on RDIES systems is therefore crucial for addressing development challenges and promoting value creation [22]. In essence, the RDIES system is a complex, dynamic, and organically structured system. It consists of digital innovation actors with biological attributes and environmental elements with non-biological characteristics. Anchored by digital infrastructure, it fosters the development of innovation platforms that enable cross-spatial and cross-boundary interaction and collaboration among diverse actors and subsystems. Through the continuous adaptation, interaction, and co-evolution of matter, information, and energy, the ecosystem evolves into a highly integrated and adaptive structure. Traditional static and linear analytical methods have proven inadequate for uncovering the underlying evolutionary dynamics of RDIES systems. In contrast, dissipative theory has become an important tool for scholars to analyze system evolution due to its unique advantages in the study of complex systems. For example, Yang Li et al. [23] conducted an empirical study on the dissipative evolution of innovation ecosystems in China’s four principal national metropolitan clusters, as well as the surrounding provinces. Yi Huiyong and Zeng Zhimo [24] examined the criteria for identifying dissipative structures in high-tech industry innovation ecosystems and characterized the process of dissipative evolution using the “global entropy–catastrophe progression” evaluation model. Li Jiaxuan and Chu Jiewang [25] developed and empirically tested a model for determining dissipative structures within intelligent digital knowledge ecosystems. Li and Jiang empirically analyzed the dissipative structural characteristics and evolutionary process of China’s digital sharing system for social public resources [26]. Therefore, dissipative structure theory provides a new and more thorough research paradigm for clarifying the workings of RDIES systems and encouraging their orderly and coordinated growth.

Therefore, this research empirically investigates the evolutionary patterns of the dissipative structure within the RDIES system guided by symbiosis theory, and illustrates the interaction mechanisms both among system actors and between these actors and their environment. The following are this study’s marginal contributions: Firstly, drawing on symbiosis theory, this study develops an evaluation index framework of “digital innovation input–digital innovation environment,” integrating key ecological elements within the context of the RDIES system as a whole. Thereby offering a novel analytical framework for exploring its evolutionary dynamics. Secondly, drawing on systems science, a dynamic evolution equation for the RDIES system was formulated using the principles of dissipative structure theory. Through the dual “global entropy–catastrophe progression” model, the dissipative evolution of the system was dynamically assessed, promoting the cross-integration of complexity science and RDIES system theory. The study highlights the dynamic characteristics and evolution of the RDIES system, offering guidance for improving the digital innovation environment, sustaining the ecosystem, and strengthening regional digital innovation. At the same time, it holds significant value for advancing sustainable regional growth, enhancing interregional digital innovation linkages and interactions.

2. Theoretical Framework

2.1. Theoretical Model Construction of RDIES Systems from the Perspective of Symbiosis Theory

The biological concept of “symbiosis” describes species’ coexistence and interdependence formed through particular interactions [27]. Natural ecosystems frequently exhibit symbiotic relationships, and RDIES systems are analogous to these natural systems in terms of their patterns and intimate ties. A variety of symbiotic relationships thus emerge from the reciprocal, interconnected, and dynamic interactions between digital innovation populations and their external environment within an RDIES system. Consequently, symbiosis theory offers a novel framework for examining the formation and evolution of RDIES systems. Drawing on the research results of Wen Xingqi [27], this study conceptualizes the RDIES system through a symbiotic lens. Within such an ecosystem, symbiotic units interact and dynamically engage through symbiotic substrates as mediators and symbiotic platforms as carriers. At the same time, they influence, adapt to, and align with the symbiotic environment. Through these processes, the ecosystem achieves networked coexistence and coordinated development.

Symbiotic units constitute the fundamental structural elements through which RDIES systems develop symbiotic relationships. The competition, cooperation, and evolutionary interactions among these units form the basis for the ecosystem’s emergence. Within the system, symbiotic units combine their unique characteristics with digital technologies to select other innovation entities that are complementary in terms of scale and function. By establishing such symbiotic relationships, the progression of digital innovation activities is significantly accelerated.

The symbiotic substrate consists of the resources accessible to symbiotic units within an RDIES system, encompassing human, material, financial, and data resources. These resources form the foundation of digital innovation activities and, due to their scarcity, serve as a critical condition for enabling and sustaining symbiotic relationships within the ecosystem. It underpins the communication and interaction among symbiotic units, while also serving as a key driver for the emergence of new logics, paradigms, and processes in digital innovation [28].

The symbiotic interface, also referred to as the symbiotic platform, constitutes the channel and carrier through which digital innovation entities within an RDIES system engage in communication and collaboration. Digital innovation entities rely on symbiotic platforms to achieve efficient connection of digital technologies. Digital users, digital innovation producers, and digital innovation complementors achieve multi-dimensional interconnection and intercommunication through symbiotic platforms [29], thereby promoting the continuous evolution of value creation and interactive coordination. As the foundational support, symbiotic platforms serve as the core medium for digital innovation populations and largely shape system efficiency and stability.

The symbiotic environment comprises all external factors that exist outside the symbiotic unit. It plays a vital role in advancing digital innovation in the region, encompassing market, policy, and economic environments. The new products and services produced by digital innovation will automatically iterate and upgrade in response to changes in the external environment because of their self-growth and dynamism qualities. A good symbiotic environment is the basic guarantee for digital innovation activities [28]. Meanwhile, well-established symbiotic relationships and a rich symbiotic substrate further contribute to the enhancement and optimization of the symbiotic environment.

2.2. Dissipative Structure Theory

In thermodynamics, the second law, or the principle of rising entropy, defines entropy as a core measure of system disorder. Positive entropy corresponds to an increase in entropy value, which means that the uncertainty of the system increases and disorder intensifies, which leads to the system gradually tending towards chaos and degradation; while negative entropy is reflected in a decrease in entropy value, which reduces the uncertainty of the system and enhances order, making it show a higher level of organization and benign state [30]. Thus, dissipative structure development is basically a process of entropy reduction through negative entropy input. Dissipative structure describes the process in which an open system, far from equilibrium, continuously exchanges matter and energy with its surroundings. Once external changes surpass a specific threshold, the system evolves from a state of chaotic disorder to an ordered state across temporal, spatial, or functional dimensions. In this non-equilibrium condition, a dissipative structure is the newly formed ordered structure [31].

Dissipative structure theory, rooted in holism and systems theory, was first widely applied in scientific disciplines such as biology and physics, and later gradually adopted in areas including economics and sociology. Its core significance is that open systems, under the influence of external environmental perturbations, can transition from a state of disorder to order through the introduction of negative entropy, eventually forming a stable and organized structure. Building on this, the evolution of RDIES systems can be viewed from a new perspective. These ecosystems are developing rapidly as regions increase investments in digital innovation, enhance infrastructure, and implement diverse policies to promote digital economic growth. During this process, the RDIES system has become somewhat chaotic and disordered due to the interweaving and interaction of different digital innovation aspects. By exchanging resources and energy with the external environment, negative entropy is generated, lowering overall disorder and enhancing system organization. This allows the components and subsystems of the RDIES system to operate collaboratively without direct external intervention, achieving higher stability and self-organization. As an RDIES system evolves into a dissipative structure, it not only strengthens sustainability and environmental adaptability but also improves overall innovation efficiency, thereby promoting high-quality and sustainable regional economic development.

3. Research Design and Model Construction

3.1. Dissipative Structure Characteristics of RDIES Systems

Four conditions are required for dissipative structures to form: openness, nonlinearity, disequilibrium, and fluctuation [32], all of which are present in RDIES systems. (1) The ecosystem is characterized by openness, maintaining its vitality and momentum through the exchange, transfer, and transformation of materials (e.g., digital innovation talent, platforms, and funding), energy (e.g., knowledge flows), and information (e.g., data related to digital innovation outcomes) with the external environment. (2) A combination of collaborative synergies and competitive dynamics exists among different digital innovation populations within the system, resulting in a range of nonlinear and non-additive interaction patterns. (3) Heterogeneity in both the innovation-driving elements and mechanisms among digital innovation actors leads to varying ecological niches in terms of technology, resources, and environment. These differences in potential energy and driving forces shape the direction and pace of ecosystem evolution. (4) Changes in external policy environments and technological advancements may, under certain conditions, disrupt the system’s original equilibrium. Upon reaching a critical threshold, such disturbances may induce fundamental structural transformations within the RDIES system, giving rise to a new state of order.

Conceptualized as an open system, the RDIES evolves through the dynamic inflow and outflow of matter, energy, and information, reflecting its continuous interaction with the external environment. These exchanges cause continuous fluctuations in the system’s entropy density, while digital innovation progressively intensifies negative entropy flow within the ecosystem. By not only counteracting internal entropy growth but also reducing overall system entropy, negative entropy flow drives the ongoing development and expansion of the RDIES system. However, as the RDIES system continuously receives substantial inputs of matter, energy, and information, its control parameters attain and surpass critical thresholds. At this point, small fluctuations are amplified, resulting in huge fluctuations. As shown in Figure 1, the RDIES system experiences a sudden transition when the negative entropy exceeds the increase in entropy and the total entropy reaches a critical threshold. At this point, small fluctuations will drive the system to transition from non-equilibrium state I to non-equilibrium state II. Huge fluctuations drive the system to transition into a dissipative structure, reaching a higher-order state. It is worth noting that such mutations and fluctuations may either optimize the system or lead to its degradation.

3.2. Overall Design Based on the Brusselator Model

The second law of thermodynamics states that for a system interacting with its environment, entropy S rises monotonically until it attains its maximum at thermodynamic equilibrium [33]. The Brusselator model was the initial reaction–diffusion framework developed to investigate chemical instabilities [34]. This model enables the quantitative analysis of self-organization phenomena within a given system. Currently, the Brusselator model has become a standard paradigm for testing whether a system exhibits dissipative structure characteristics [35]. It has been extensively applied in studies of innovation ecosystems [23,36], construction industry systems [37,38], and digital sharing platforms for social public resources [26]. Building on this foundation, the model is used here to examine the self-organizing behavior of the RDIES system.

(1)

The Brusselator Model

The Brusselator model is mathematically described by the following equations [39]:

$$\left\{\begin{array}{l}A\stackrel{k_1}{\to }x\\ B+x\stackrel{k_2}{\to }y+D\\ 2x+y\stackrel{k_3}{\to }3x\\ x\stackrel{k_4}{\to }E\end{array}\right.$$

(1)

In the above equation, A and B represent the initial reactants, continuously supplied by the external environment to maintain constant concentrations. D and E denote the reaction products, which are removed immediately after formation. x and y denote intermediate species, whose concentrations change dynamically during the reaction. The catalysts k₁, k₂, k₃, and k₄ directly influence the overall reaction rate. Based on Equation (1), stability analysis is employed to detect potential instabilities in the system, serving as the foundation for determining its evolution toward a dissipative structure. Drawing on the bivariate differential equation model proposed by Ren et al. [40], a set of evolutionary dynamic equations for variables x and y is constructed, as shown in Equation (2):

$$\left\{\begin{array}{l}{\displaystyle \frac{dx}{dt}}=k_{1}A-k_{2}Bx+k_3{x}^{2}y-k_{4}x+M_1{\displaystyle \frac{d^{2}x}{d^{2}t}}\hfill \\ {\displaystyle \frac{dy}{dt}}=k_{2}Bx-k_3{x}^{2}y+M_2{\displaystyle \frac{d^{2}y}{d^{2}t}}\hfill \end{array}\right.$$

(2)

Ignoring the influence of the diffusion terms $M_1{\displaystyle \frac{d^{2}x}{d^{2}t}}$, $M_2{\displaystyle \frac{d^{2}y}{d^{2}t}}$, and further setting $k_1=k_2=k_3=k_4=1$, then Equation (2) is simplified to:

$$\left\{\begin{array}{l}{\displaystyle \frac{dx}{dt}}=A-Bx+x^{2}y-x\hfill \\ {\displaystyle \frac{dy}{dt}}=Bx-x^{2}y\hfill \end{array}\right.$$

(3)

$$\left\{\begin{array}{l}A-Bx+x^{2}y-x=0\hfill \\ Bx-x^{2}y=0\hfill \end{array}\right.$$

(4)

The steady-state solutions of the dynamic system represented in Equation (2), as formulated in Equation (4), are given by: $x_0=A$, $y_0=B/A$. It should be emphasized that x and y represent only two chemical components and do not directly indicate the system’s degree of order. On this basis, an RDIES system can develop a dissipative structure only by evolving from a non-steady to a steady state. Therefore, the key lies in determining the critical threshold at which the system undergoes a sudden change. Based on this, let $x=x_0+\Delta x$, $y=y_0+\Delta y$, $f_1(x,y)=A-Bx+x^{2}y-x$, $f_2(x,y)=Bx-x^{2}y$, $f_{1x}(x_0,y_0)=B-1$, $f_{1y}(x_0,y_0)=A^2$, $f_{2x}(x_0,y_0)=-B$, $f_{2y}(x_0,y_0)=-A^2$. Then Equation (4) can be linearized at the stable state solutions $(x_0,y_0)$, resulting in Equation (5).

$$\left\{\begin{array}{l}{\displaystyle \frac{d\Delta x}{dt}}=(B-1)\Delta x+A^2\Delta y\\ {\displaystyle \frac{d\Delta y}{dt}}=-B\Delta x-A^2\Delta y\end{array}\right.$$

(5)

The characteristic equation for the linearized form of differential Equation (5) is given by: ${\lambda }^2-\omega \lambda +T=0$, where $\omega =B-1-A^2$, $T=A^2>0$, ${\lambda }_{1,2}={\displaystyle \frac{\omega \pm \sqrt{{\omega }^2-4a^2}}{2}}$. The detailed solution of the characteristic equation is provided in

Table 1. Five typical states of system dissipation evolution.

Number	Condition	Result
1	When $\omega <0$, ${\omega }^2>4a^2$, ${\lambda }_{1,2}$ are the negative real roots.	The system is stable, $(x_0,y_0)$ is a stable equilibrium point.
2	When $\omega >0$, ${\omega }^2>4a^2$, ${\lambda }_{1,2}$ are positive real roots.	The system deviates from the steady state, $(x_0,y_0)$ is an unstable equilibrium point.
3	When $\omega <0$, ${\omega }^2<4a^2$, ${\lambda }_{1,2}$ are complex conjugate roots with negative real parts.	The system converges, $(x_0,y_0)$ is a stable focus.
4	When $\omega >0$, ${\omega }^2<4a^2$, ${\lambda }_{1,2}$ are complex conjugate roots with positive real parts.	The system oscillates, $(x_0,y_0)$ is an unstable focus.
5	When $\omega =0$, the system has purely imaginary roots.	The system is in a critical state.

. It can be inferred that the stability of the steady-state solution $(x_0,y_0)$ depends on the relationship between $\omega$ and $T$, which corresponds to the relationship between parameters A and B. When $\omega \le 0$, the system remains in a stable state, it represents a low-efficiency and disordered structure. In contrast, when $\omega >0$, the system loses stability and begins to evolve toward an ordered dissipative structure. Thus, the condition for the emergence of a dissipative structure can be expressed as Equation (6):

$$\left\{\begin{array}{l}B<1+A^2, \mathrm{the} \mathrm{system} \mathrm{is} \mathrm{stable} \mathrm{and} \mathrm{has} \mathrm{a} \text{non-dissipative} \mathrm{structure}.\\ B>1+A^2, \mathrm{the} \mathrm{stationary} \mathrm{state} \mathrm{solution} \mathrm{is} \mathrm{in} \mathrm{a} \text{non-stationary} \mathrm{state} \mathrm{and} \\ \mathrm{the} \mathrm{system} \mathrm{can} \mathrm{form} \mathrm{adissipative} \mathrm{structure}.\\ B=1+A^2, \mathrm{the} \mathrm{system} \mathrm{is} \mathrm{in} \mathrm{a} \mathrm{critical} \mathrm{state}.\end{array}\right.$$

(6)

The quantitative determination of whether a system has developed a dissipative structure is made possible by Equation (6); however, it fails to reveal the specific mechanisms through which the control variables—A (digital innovation investment) and B (digital innovation environment)—influence the formation of such structures. This constraint limits a full understanding of the system’s evolutionary dynamics. Catastrophe theory, however, suggests that adjusting control variables can trigger an abrupt shift from a stable, disordered state to a dissipative structure. The system’s dissipative evolution follows a trajectory of “equilibrium–disequilibrium–dynamic equilibrium,” providing a basis for applying catastrophe theory [24]. Accordingly, this study integrates the catastrophe progression method with the global entropy method to construct a “global entropy–catastrophe progression” evaluation model, which clarifies how control variables A and B influence the system’s dissipative evolution. A comprehensive assessment of these variables is then conducted using the global entropy method, as detailed below.

Assume that there are n evaluation indicators. For m regions and t years, the j-th indicator is evaluated accordingly. The cross-sectional data matrix $X^t={(x_{ij})}_{m\times n}$ can be obtained for each year. These t cross-sectional matrices are arranged in chronological order from top to bottom, thereby constructing a global evaluation matrix of $NT\times M$, denoted as:

$$X={(X^1,X^2,\dots ,X^t{)}^{\prime }}_{mt\times n}={(x_{ij})}_{mt\times n}$$

(7)

The data in the global evaluation matrix X are standardized as follows:

$$x_{ij}^{\prime }={\displaystyle \frac{x_{ij}-\underset{t}{\min }{x}_{ij}}{\underset{t}{\max }{x}_{ij}-\underset{t}{\min }{x}_{ij}}}\times 0.99+0.01,1\le i\le mt,1\le j\le n,1\le t\le T$$

(8)

The proportion of the i-th region under the j-th indicator in the global evaluation matrix is calculated as:

$$p_{ij}={\displaystyle \frac{x_{ij}^{\prime }}{{\displaystyle \sum _{i=1}^{mt}{x}_{ij}^{\prime }}}}$$

(9)

Assess the relative importance of each indicator using the global entropy method as follows:

$$e_{Aj}=-{\displaystyle \frac{1}{\ln (mt)}}{\displaystyle \sum _{i=1}^{mt}pij}\ln pij$$

(10)

Calculate the divergence coefficient of the j-th indicator:

$$g_{Aj}=1-e_{Aj}$$

(11)

Calculate the entropy weight of each indicator:

$$q_{Aj}={\displaystyle \frac{g_{Aj}}{{\displaystyle \sum _{i=1}^{mt\times n}{g}_{Aj}}}}$$

(12)

Calculate the entropy values of A and B, respectively:

$$E_A={\displaystyle \sum _{i=1}^{mt\times n}{q}_{Ai}{e}_{Ai}},E_B={\displaystyle \sum _{i=1}^{mt\times n}{q}_{Bi}{e}_{Bi}}$$

(13)

In the catastrophe series model, the details are shown in

Table 2. Potential function and normalization formula of the mutation system evaluation model.

Mutation Type	Indicator Count	Potential Function	Normalization Formula
Fold catastrophe	1	$V(x)={\displaystyle \frac{1}{3}}{x}^3+ax$	$x_a=\sqrt{a}$
Cusp catastrophe	2	$V(x)=x^4+a{x}^2+bx$	$x_a=\sqrt{a}$$, x_b=\sqrt[3]{b}$
Swallowtail catastrophe	3	$V(x)=x^5+{\displaystyle \frac{1}{3}}a{x}^3+{\displaystyle \frac{1}{2}}b{x}^2+cx$	$x_a=\sqrt{a}$$, x_b=\sqrt[3]{b}$$, x_c=\sqrt[4]{c}$
Butterfly catastrophe	4	$V(x)={\displaystyle \frac{1}{6}}{x}^6+{\displaystyle \frac{1}{4}}a{x}^4+{\displaystyle \frac{1}{3}}b{x}^3+{\displaystyle \frac{1}{2}}c{x}^2+dx$	$x_a=\sqrt{a}$$, x_b=\sqrt[3]{b}$$, x_c=\sqrt[4]{c}$$, x_d=\sqrt[5]{d}$

, where x is the stage variable, and a, b, c, and d are indicator variables.

(2)

Translation of the RDIES System Based on the Brusselator Model

In the translation of the Brusselator model, A and B represent regional digital innovation investment and the regional digital innovation environment (symbiotic environment), respectively. D represents the revenue generated by the RDIES system (digital innovation performance), and E represents the output of regional digital innovation activities (dissipative structure). x and y, respectively, represent state variables, such as digital innovation achievements and the ability to transform digital innovation achievements.

$A\stackrel{k_1}{⟶}x$. This reaction represents a nonlinear and dynamic mechanism whereby digital innovation inputs are transformed into outputs, through which the RDIES system ultimately generates innovation outcomes by leveraging digital human resources, mobilizing financial capital, and fostering the construction of digital innovation platforms.

$B+x\stackrel{k_2}{⟶}y+D$. The reaction illustrates the effect of the digital innovation environment on the results of digital innovation. Preliminary outcomes from digital innovation resources undergo market-oriented transformation through interaction with the innovation environment, ultimately realizing digital innovation performance.

$2x+y\stackrel{k_3}{⟶}3x$. This reaction represents the positive market feedback effect of the capability to translate digital innovation outcomes into the advancement of those outcomes. In other words, an enhanced capacity for transforming digital innovation results stimulates the growth and upgrading of market demand, which in turn incentivizes digital innovation enterprises to increase their investment in innovation, thus improving both the quantity and quality of digital innovation outcomes.

$x\stackrel{k_4}{⟶}E$. The reaction reflects the metabolic and dissipative evolution of the RDIES system, suggesting that interactions between the digital innovation environment and investment guide the system toward a higher-order dissipative structure.

3.3. Model Construction, Indicator Selection, and Data Sources

Building upon the work of Yang Li et al. [23], a “global entropy–catastrophe progression” evaluation model is developed in this study to analyze the dissipative evolution of RDIES systems. The methodological procedure is outlined as follows: First, an evaluation framework is systematically designed within the two-dimensional structure of “A (digital innovation investment)—B (digital innovation environment)” to rigorously capture and characterize the dissipative evolutionary dynamics of RDIES systems. Second, to maintain the scientific validity and comparability of the results, all indicators are made dimensionless, and their weights are calculated using the global entropy method. Third, each sample system’s formation of a dissipative structure is assessed using the dissipative structure judgment conditions. Finally, the evolution process of the dissipative structure is thoroughly examined using the catastrophe progression method to uncover the system’s evolution law. The translated Brusselator model suggests that the dissipative evolution of RDIES systems is primarily governed by two critical factors: A and B. For digital innovation investment, this study constructs evaluation indicators from the following three aspects. (1) Digital innovation population (symbiotic unit): A complex system, the RDIES system is made up of symbiotic entities, including enterprises, universities, and scientific research institutions [41]. This study measures the digital innovation population using three indicators: the number of general universities, the number of R&D institutions in industrial enterprises above a certain scale, and the number of large-scale industrial enterprises actively engaged in R&D. (2) Digital innovation resources (symbiotic matrix): Symbiotic units in an RDIES system possess various resources that power value creation within the system. Digital innovation human resources are quantified in this study using employment figures in the information transmission, software, and IT service industries; the amount of fixed asset investment in the information transmission, software, and information technology service industries to represent digital innovation material resources; internal expenditures on digital industry R&D funds to represent digital innovation financial resources; and the average number of bytes on a web page to measure the level of data resources. (3) Digital innovation platform (symbiotic platform): Digital infrastructure and the digital platforms it supports are crucial pillars in the growth of RDIES systems and are necessary for the ecosystems to function properly. The network access carrying capacity of regional information resources, as well as the degree of data sharing and use, have greatly increased with the ongoing development of digital infrastructure and new digital innovation platforms [42]. Accordingly, this research analyzes relevant indicators across digital infrastructure and new digital innovation platforms. The support capacity of digital infrastructure is measured by broadband access ports, mobile switch capacity, and the length of long-distance optical cables. New digital innovation platforms are represented by the number of IoT, cloud computing, blockchain, and data center companies, indicating their contribution to digital technology innovation [43].

Given that the B variable in the Brusselator model represents the support provided by the digital innovation environment, this study primarily measures the digital innovation environment (symbiotic environment) across three dimensions: (1) Economic Environment: The economic environment plays a pivotal guiding and supportive role in facilitating digital innovation activities. This study uses GDP per capita, per capita consumer expenditure, and the digital financial inclusion index to assess the economic environment. (2) Policy environment: Digital innovation activities are closely dependent on policy support and guidance. In particular, the frequency of pertinent policy supply terms for digital economic development, the percentage of science and technology spending in the overall public budget, and local fiscal education spending are used to gauge the policy environment [44]. (3) Market environment: Fostering a robust market environment facilitates the commercialization of digital innovation outcomes and enhances the economic returns generated by the digital innovation ecosystem. The market environment is specifically measured in this article by the number of technology market transaction contracts, the volume of technology market transactions, and the per capita retail sales of social consumer goods. Therefore, a two-dimensional framework based on a “digital innovation investment-digital innovation environment” is constructed, and combined with the core ecological elements of symbiotic units, symbiotic matrix, symbiotic platform, and symbiotic environment, corresponding indicators such as “symbiotic unit-digital innovation population” and “symbiotic matrix-digital innovation resource investment”, “symbiotic platform-digital innovation platform construction” and “symbiotic environment-economic, policy, and market environment” are added, as displayed in

Table 3. Brusselator model evaluation index system of the RDIES system.

Target Layer	Rule Layer	Index Layer
A Digital innovation investment	Digital innovation population X1	Number of higher education institutions X11
		Number of industrial enterprises with R&D activities X12
		Number of research and development institutions in industrial enterprises X13
	Digital innovation resource investment X2	Number of employees in the information transmission, software, and information technology services sector X21
		Fixed asset investment in the information transmission, software, and information technology services sector X22
		Internal expenditure on research and development in the digital industry X23
		Average byte size per web page X24
	Digital innovation platform construction X3	Number of internet broadband access ports X31
		Mobile phone exchange capacity X32
		Length of long-distance optical cable lines X33
		Number of enterprises specializing in IoT, cloud computing, blockchain, and data centers X34
B Digital innovation environment	Economic environment Y1	GDP per capita Y11
		Digital financial inclusion index Y12
		Per capita consumption expenditure of residents Y13
	Policy environment Y2	Proportion of science and technology expenditure in the general public budget spending Y21
		Local financial expenditure for education Y22
		Proportion of digital word frequency in government bulletins Y23
	Market environment Y3	Technology market turnover Y31
		Number of technology market contracts Y32
		Per capita retail sales of consumer goods Y33

.

This study examines 30 provincial-level regions in China over the period of 2013–2023. Missing observations were systematically addressed using a combination of moving average interpolation, nearest-neighbor imputation, and mean value substitution to ensure data completeness and consistency. Referring to existing research [45], the digital industry in the indicator system of this paper uses relevant data from the computer and office equipment manufacturing industry and the electronic and communication equipment manufacturing industry. Data for this study were collected from the China Statistical Yearbook, China Science and Technology Statistical Yearbook, China Torch Statistical Yearbook, China High-tech Industry Statistical Yearbook, official websites of the National Bureau of Statistics and the Digital Finance Research Center of Peking University, and provincial and municipal government portals. Information on companies involved in IoT, cloud computing, blockchain, and data centers was obtained from the Qichacha platform.

4. Empirical Analysis

4.1. Determination of System Dissipative Structure

Using the indicators in Table 3, raw data were collected and processed to derive the A and B values of the digital innovation ecosystem’s dissipative structure for each sample region. The dissipative structure was then determined according to Formula (6). Concerning relevant literature [23], let $k_1=k_2=k_3=k_4=1$.

(1) Overall analysis.

Table 4. Results of the determination of the dissipative structure of the RDIES system.

Region	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023	Average
Beijing	−0.570	−0.525	−0.525	−0.503	−0.450	−0.412	−0.329	−0.331	−0.269	−0.256	−0.209	−0.398
Tianjin	−0.798	−0.780	−0.768	−0.762	−0.752	−0.737	−0.723	−0.735	−0.713	−0.723	−0.691	−0.744
Hebei	−0.936	−0.932	−0.924	−0.902	−0.896	−0.885	−0.879	−0.867	−0.845	−0.842	−0.812	−0.884
Shanxi	−0.930	−0.927	−0.932	−0.925	−0.891	−0.887	−0.885	−0.878	−0.848	−0.864	−0.840	−0.891
Inner Mongolia	−0.925	−0.916	−0.905	−0.894	−0.894	−0.889	−0.897	−0.891	−0.874	−0.862	−0.845	−0.890
Liaoning	−0.869	−0.860	−0.859	−0.852	−0.844	−0.827	−0.834	−0.826	−0.800	−0.804	−0.767	−0.831
Jilin	−0.927	−0.922	−0.897	−0.885	−0.877	−0.867	−0.876	−0.875	−0.869	−0.889	−0.854	−0.885
Heilongjiang	−0.939	−0.931	−0.920	−0.904	−0.892	−0.885	−0.902	−0.897	−0.874	−0.861	−0.869	−0.898
Shanghai	−0.709	−0.701	−0.704	−0.673	−0.651	−0.617	−0.569	−0.578	−0.500	−0.489	−0.395	−0.599
Jiangsu	−0.834	−0.860	−0.837	−0.852	−0.820	−0.818	−0.816	−0.805	−0.717	−0.758	−0.706	−0.802
Zhejiang	−0.838	−0.836	−0.831	−0.811	−0.813	−0.797	−0.754	−0.785	−0.739	−0.771	−0.620	−0.781
Anhui	−0.909	−0.897	−0.869	−0.824	−0.817	−0.796	−0.746	−0.751	−0.677	−0.641	−0.609	−0.776
Fujian	−0.893	−0.886	−0.872	−0.855	−0.845	−0.820	−0.788	−0.775	−0.751	−0.747	−0.736	−0.815
Jiangxi	−0.945	−0.931	−0.910	−0.896	−0.876	−0.878	−0.845	−0.836	−0.795	−0.800	−0.730	−0.858
Shandong	−0.868	−0.859	−0.842	−0.829	−0.814	−0.770	−0.749	−0.659	−0.692	−0.695	−0.659	−0.767
Henan	−0.926	−0.916	−0.909	−0.900	−0.886	−0.871	−0.845	−0.837	−0.786	−0.775	−0.750	−0.855
Hubei	−0.881	−0.830	−0.807	−0.779	−0.755	−0.741	−0.694	−0.695	−0.632	−0.569	−0.465	−0.713
Hunan	−0.919	−0.920	−0.910	−0.898	−0.883	−0.857	−0.835	−0.805	−0.774	−0.689	−0.625	−0.829
Guangdong	−0.831	−0.856	−0.832	−0.841	−0.899	−0.913	−0.894	−0.991	−1.079	−1.140	−1.162	−0.949
Guangxi	−0.944	−0.931	−0.921	−0.916	−0.903	−0.904	−0.879	−0.881	−0.849	−0.861	−0.858	−0.895
Hainan	−0.950	−0.943	−0.930	−0.917	−0.910	−0.908	−0.882	−0.877	−0.846	−0.833	−0.811	−0.891
Chongqing	−0.916	−0.902	−0.894	−0.874	−0.873	−0.838	−0.820	−0.806	−0.773	−0.759	−0.721	−0.834
Sichuan	−0.920	−0.909	−0.894	−0.888	−0.878	−0.852	−0.824	−0.816	−0.784	−0.800	−0.762	−0.848
Guizhou	−0.963	−0.953	−0.926	−0.890	−0.867	−0.860	−0.850	−0.853	−0.835	−0.835	−0.819	−0.878
Yunnan	−0.955	−0.950	−0.937	−0.915	−0.912	−0.907	−0.865	−0.865	−0.853	−0.862	−0.840	−0.896
Shaanxi	−0.890	−0.863	−0.856	−0.845	−0.800	−0.777	−0.732	−0.731	−0.655	−0.628	−0.583	−0.760
Gansu	−0.960	−0.954	−0.931	−0.928	−0.916	−0.915	−0.904	−0.894	−0.863	−0.866	−0.844	−0.907
Qinghai	−0.971	−0.958	−0.945	−0.939	−0.933	−0.915	−0.915	−0.910	−0.893	−0.915	−0.900	−0.927
Ningxia	−0.955	−0.941	−0.919	−0.922	−0.903	−0.888	−0.874	−0.875	−0.861	−0.869	−0.849	−0.896
Xinjiang	−0.945	−0.938	−0.931	−0.928	−0.916	−0.914	−0.904	−0.902	−0.884	−0.870	−0.853	−0.908
National average	−0.894	−0.884	−0.871	−0.858	−0.846	−0.831	−0.810	−0.808	−0.778	−0.776	−0.739	−0.827

Note: The values in the table represent $B-1-A^2$. A value greater than 0 indicates the formation of a dissipative structure, while a value less than 0 indicates that no such structure has formed.

and Figure 2 show that the dissipative structure value of China’s RDIES systems rose from −0.894 to −0.739 over the observation period, indicating a gradual evolution toward a dissipative structure. These findings indicate that China’s RDIES systems experienced a notable improvement between 2013 and 2023. But the dissipative values of RDIES systems in the sample regions from 2013 to 2023 are consistently less than zero, indicating that a dissipative structure has not yet formed in these regions. The result suggests that internal entropy growth in the RDIES system exceeds the input of external negative entropy, or that the negative entropy has not attained the threshold required to establish a dissipative structure. This reflects insufficient coordination between regional digital innovation investment and the innovation environment.

(2) Regional comparison. Figure 3 shows that the dissipative structure value of RDIES systems in the eastern region exceeds the national average. The dissipative structure value in the central region has increased markedly. After 2019, the dissipation structure judgment value has been higher than the national average. The dissipative structure values in the western and northeastern regions remain below the national average.

(3) Analysis of special provinces and cities. As shown in Table 4 and Figure 2, from 2013 to 2023, Beijing’s digital innovation ecosystem had the highest dissipation structure judgment value among all provinces in China. This is because Beijing has actively developed into a global benchmark city for the digital economy, concentrating substantial digital innovation resources and attracting significant digital talent. Beijing’s strong economic development and mature technology market have further propelled digital industry innovation, serving as key drivers of its RDIES system’s gradual enhancement. The dissipation level of Guangdong Province’s RDIES system declined significantly between 2019 and 2023, indicating a serious imbalance in the ecosystem. Positive entropy flows have persisted within the system without being neutralized, increasing systemic disorder. This, in turn, weakens the ecosystem’s driving force for innovation and the economy. This is closely linked to Guangdong Province’s digital economy policies, including the expansion of digital infrastructure and the coordinated growth of digital industries. It also suggests that Guangdong Province needs to shift its approach to building a digital innovation ecosystem, shifting from solely increasing digital innovation resource investment to fostering synergy between digital innovation resource investment and the digital innovation environment. This approach should foster positive interactions between digital innovation actors and between them and the digital innovation environment, neutralizing system entropy flows and thereby increasing dissipation levels. Hubei Province is a leader in digital innovation and development in the central region. Indicating that Hubei Province’s digital innovation and development has created a powerful radiating effect on the neighboring provinces and cities, the dissipation structure determination values of Hunan Province, Anhui Province, Henan Province, and Shaanxi Province are relatively high. There is a gradual increase in the dissipation level of RDIES systems in the western area. Although its impact on digital innovation in neighboring areas is not immediately evident, Shaanxi Province shows the highest dissipation level among the western provinces. In the northeast, the dissipation level of the RDIES system exhibits a fluctuating upward trend, with Liaoning Province performing strongly, while Jilin and Heilongjiang provinces lag.

4.2. Comprehensive Assessment of System Dissipative Evolution

By applying dissipative structure analysis and catastrophe theory, this study evaluates regional digital innovation investment and the innovation environment to investigate the dissipative evolution of RDIES systems. The process begins with data normalization, followed by the application of the global entropy method to determine indicator weights. Further, based on the Stata17 analysis results, sub-indicators that are related are complementary types, and those that are not linked are non-complementary types. As shown in

Table 5. Analysis results of index weights and mutation types.

Objective Level	Variable Level	Indexes	Weight
A Digital innovation investment (Swallowtail catastrophe) (Complementary type)	X1 (Swallowtail catastrophe) (Complementary type) 0.3559	X11	0.0292
		X12	0.1402
		X13	0.1865
	X2 (Butterfly catastrophe) (Non-complementary type) 0.3691	X21	0.1071
		X22	0.0595
		X23	0.1745
		X24	0.0280
	X3 (Butterfly catastrophe) (Complementary type) 0.2750	X31	0.0525
		X32	0.0474
		X33	0.0556
		X34	0.1195
B Digital innovation environment (Swallowtail catastrophe) (Complementary type)	Y1 (Swallowtail catastrophe) (Complementary type) 0.1952	Y11	0.0797
		Y12	0.0465
		Y13	0.0690
	Y2 (Swallowtail catastrophe) (Non-complementary type) 0.2562	Y21	0.1180
		Y22	0.0768
		Y23	0.0614
	Y3 (Swallowtail catastrophe) (Complementary type) 0.5486	Y31	0.2674
		Y32	0.2067
		Y33	0.0744

, specifically. Based on Table 5, it can be further obtained that:

(1) For X₁, there are three measurement indicators: X₁₁, X₁₂, and X₁₃, with weights of 0.0292, 0.1402, and 0.1865, respectively. From this, it can be known that $Q_{13}>Q_{12}>Q_{11}$, $X_1=({X_{13}}^{{\displaystyle \frac{1}{2}}}+{X_{12}}^{{\displaystyle \frac{1}{3}}}+{X_{11}}^{{\displaystyle \frac{1}{4}}})/3$.

(2) For X₂, there are four measurement indicators: X₂₁, X₂₂, X₂₃, and X₂₄, with weights of 0.1071, 0.0595, 0.1745, and 0.0280, respectively. From this, it can be known that $Q_{23}>Q_{21}>Q_{22}>Q_{24}$, $X_2=\min ({X_{23}}^{{\displaystyle \frac{1}{2}}},{X_{21}}^{{\displaystyle \frac{1}{3}}},{X_{22}}^{{\displaystyle \frac{1}{4}}},{X_{24}}^{{\displaystyle \frac{1}{5}}}).$

(3) For X₃, there are four measurement indicators: X₃₁, X₃₂, X₃₃, and X₃₄, with weights of 0.0525, 0.0474, 0.0556, and 0.1195, respectively. From this, it can be known that $Q_{34}>Q_{33}>Q_{31}>Q_{32}$, $X_3=({X_{34}}^{{\displaystyle \frac{1}{2}}}+{X_{33}}^{{\displaystyle \frac{1}{3}}}+{X_{31}}^{{\displaystyle \frac{1}{4}}}+{X_{32}}^{{\displaystyle \frac{1}{5}}})/4$.

From the preceding analysis, the evaluation value of A (Digital innovation investment) can be obtained, $Q_2>Q_1>Q_3$, $A=({X_2}^{{\displaystyle \frac{1}{2}}}+{X_1}^{{\displaystyle \frac{1}{3}}}+{X_3}^{{\displaystyle \frac{1}{4}}})/3$. Similarly, the evaluation value of B (Digital innovation environment) can be calculated. The calculation results are summarized in

Table 6. Evaluation value of the regional digital innovation investment.

Region	Evaluation Value of the Regional Digital Innovation Investment
	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023
Beijing	0.670	0.680	0.688	0.694	0.695	0.694	0.694	0.704	0.713	0.732	0.747
Tianjin	0.633	0.637	0.646	0.648	0.652	0.655	0.651	0.661	0.668	0.674	0.675
Hebei	0.647	0.653	0.664	0.670	0.679	0.680	0.686	0.706	0.701	0.715	0.716
Shanghai	0.675	0.680	0.684	0.687	0.688	0.689	0.700	0.722	0.747	0.741	0.756
Jiangsu	0.785	0.800	0.804	0.815	0.825	0.838	0.855	0.871	0.883	0.899	0.900
Zhejiang	0.737	0.748	0.766	0.776	0.787	0.796	0.807	0.827	0.841	0.855	0.861
Fujian	0.689	0.715	0.708	0.717	0.730	0.743	0.749	0.760	0.776	0.787	0.791
Shandong	0.719	0.733	0.739	0.748	0.756	0.755	0.751	0.766	0.785	0.806	0.812
Guangdong	0.826	0.834	0.857	0.880	0.903	0.914	0.925	0.936	0.946	0.947	0.948
Hainan	0.565	0.575	0.573	0.576	0.579	0.586	0.588	0.597	0.605	0.604	0.609
Shanxi	0.619	0.613	0.622	0.631	0.638	0.643	0.647	0.658	0.658	0.662	0.661
Anhui	0.669	0.684	0.694	0.706	0.719	0.729	0.738	0.754	0.771	0.782	0.790
Jiangxi	0.634	0.632	0.649	0.661	0.681	0.696	0.711	0.730	0.742	0.752	0.751
Henan	0.656	0.663	0.678	0.691	0.698	0.700	0.709	0.722	0.739	0.752	0.748
Hubei	0.680	0.690	0.700	0.707	0.716	0.726	0.738	0.749	0.770	0.789	0.791
Hunan	0.668	0.672	0.687	0.689	0.703	0.713	0.718	0.733	0.751	0.763	0.773
Inner Mongolia	0.606	0.602	0.612	0.619	0.625	0.626	0.624	0.629	0.638	0.646	0.652
Guangxi	0.619	0.618	0.625	0.631	0.638	0.641	0.645	0.657	0.670	0.677	0.672
Chongqing	0.621	0.633	0.645	0.657	0.667	0.675	0.684	0.702	0.711	0.717	0.715
Sichuan	0.672	0.676	0.695	0.708	0.723	0.732	0.731	0.744	0.761	0.772	0.775
Guizhou	0.607	0.617	0.618	0.627	0.634	0.638	0.643	0.651	0.652	0.666	0.666
Yunnan	0.616	0.622	0.626	0.631	0.636	0.642	0.649	0.656	0.669	0.680	0.693
Shaanxi	0.633	0.637	0.653	0.660	0.667	0.673	0.679	0.693	0.704	0.706	0.712
Gansu	0.599	0.604	0.609	0.612	0.619	0.622	0.626	0.629	0.633	0.635	0.640
Qinghai	0.547	0.557	0.559	0.563	0.562	0.566	0.566	0.568	0.572	0.576	0.576
Ningxia	0.559	0.567	0.566	0.573	0.580	0.586	0.592	0.595	0.606	0.612	0.611
Xinjiang	0.602	0.610	0.611	0.615	0.616	0.620	0.621	0.627	0.630	0.633	0.636
Liaoning	0.648	0.654	0.657	0.654	0.661	0.666	0.670	0.677	0.685	0.691	0.689
Jilin	0.605	0.612	0.609	0.615	0.618	0.621	0.621	0.624	0.629	0.631	0.629
Heilongjiang	0.617	0.621	0.623	0.628	0.631	0.630	0.633	0.637	0.637	0.639	0.638

and

Table 7. Evaluation value of the regional digital innovation environment.

Region	Evaluation Value of the Regional Digital Innovation Environment
	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023
Beijing	0.867	0.877	0.887	0.898	0.900	0.906	0.932	0.933	0.942	0.945	0.955
Tianjin	0.794	0.805	0.810	0.815	0.813	0.817	0.817	0.811	0.824	0.827	0.836
Hebei	0.698	0.703	0.692	0.727	0.727	0.728	0.738	0.755	0.779	0.779	0.801
Shanghai	0.825	0.835	0.842	0.850	0.858	0.868	0.888	0.885	0.904	0.914	0.929
Jiangsu	0.805	0.807	0.849	0.857	0.860	0.876	0.888	0.897	0.922	0.933	0.941
Zhejiang	0.781	0.795	0.825	0.837	0.847	0.857	0.876	0.886	0.904	0.905	0.940
Fujian	0.764	0.768	0.773	0.779	0.794	0.805	0.826	0.835	0.848	0.848	0.850
Shandong	0.778	0.786	0.794	0.801	0.817	0.826	0.845	0.868	0.887	0.875	0.890
Guangdong	0.817	0.820	0.843	0.857	0.870	0.874	0.896	0.907	0.920	0.913	0.919
Hainan	0.670	0.679	0.691	0.702	0.694	0.692	0.732	0.736	0.749	0.752	0.766
Shanxi	0.715	0.720	0.700	0.700	0.728	0.728	0.725	0.737	0.770	0.735	0.757
Anhui	0.737	0.747	0.775	0.786	0.803	0.815	0.833	0.838	0.864	0.879	0.889
Jiangxi	0.688	0.707	0.723	0.737	0.762	0.765	0.789	0.803	0.823	0.834	0.855
Henan	0.704	0.710	0.716	0.728	0.755	0.762	0.787	0.804	0.839	0.853	0.857
Hubei	0.763	0.797	0.813	0.828	0.838	0.847	0.864	0.863	0.881	0.897	0.917
Hunan	0.709	0.718	0.723	0.728	0.752	0.768	0.797	0.822	0.843	0.874	0.891
Inner Mongolia	0.695	0.701	0.707	0.700	0.705	0.667	0.674	0.692	0.711	0.713	0.749
Guangxi	0.692	0.712	0.701	0.698	0.717	0.719	0.727	0.727	0.766	0.768	0.763
Chongqing	0.722	0.725	0.730	0.742	0.749	0.760	0.777	0.783	0.809	0.816	0.825
Sichuan	0.712	0.727	0.742	0.748	0.757	0.778	0.798	0.809	0.841	0.827	0.836
Guizhou	0.619	0.660	0.689	0.706	0.736	0.739	0.765	0.766	0.775	0.773	0.772
Yunnan	0.656	0.669	0.686	0.687	0.700	0.699	0.714	0.723	0.739	0.738	0.753
Shaanxi	0.727	0.749	0.764	0.774	0.797	0.801	0.805	0.794	0.843	0.846	0.863
Gansu	0.645	0.664	0.691	0.687	0.691	0.679	0.695	0.711	0.732	0.750	0.767
Qinghai	0.627	0.658	0.669	0.673	0.686	0.681	0.657	0.664	0.695	0.642	0.671
Ningxia	0.642	0.658	0.677	0.685	0.697	0.699	0.719	0.723	0.731	0.736	0.743
Xinjiang	0.683	0.688	0.688	0.693	0.688	0.682	0.685	0.684	0.705	0.698	0.721
Liaoning	0.755	0.787	0.778	0.772	0.771	0.783	0.775	0.777	0.795	0.785	0.798
Jilin	0.719	0.725	0.733	0.741	0.758	0.751	0.730	0.736	0.731	0.673	0.726
Heilongjiang	0.703	0.713	0.716	0.721	0.727	0.715	0.706	0.718	0.736	0.732	0.729

.

(1) The evaluation results indicate that digital innovation investment in the sample regions demonstrated an overall upward trend from 2013 to 2023. Guangdong Province has the highest average digital innovation investment in the country, owing to its well-developed digital innovation platforms, which provide a solid foundation for innovation entities to engage in digital innovation activities. In contrast, Qinghai Province ranks last nationwide in average digital innovation investment, primarily due to its significantly lagging digital infrastructure, particularly the extremely low value of mobile telephone switch capacity. Zhejiang Province experienced the fastest growth in digital innovation investment, with its evaluation score rising from 0.737 in 2013 to 0.861 in 2023, marking a 16.8% increase. This rapid growth can be attributed to the province’s strong R&D capacity and infrastructure. In 2023, Zhejiang placed second nationally in R&D institutions of large-scale industrial enterprises and third in long-distance optical cable length. The results suggest that growth in digital innovation entities and improved digital infrastructure are primary factors affecting digital innovation investment evaluation.

(2) According to the evaluation results, the assessment values of the digital innovation environment in the sample regions fluctuated but increased overall from 2013 to 2023. The average evaluation value of Beijing’s digital innovation environment ranks first in the country. The digital innovation environment is excellent, especially in 2023, when indicators such as GDP per capita, transaction volume of the technology market, and the number of technology market contracts all ranked first in the country. Qinghai Province ranks lowest in China in terms of the average digital innovation environment, largely due to its particularly weak technology market transaction volume. The market environment remains in urgent need of improvement. In Hunan, the digital innovation environment value rose from 0.709 in 2013 to 0.891 in 2023, the fastest growth rate at 25.7%. The rise is mainly driven by notable improvements in the digital inclusive finance index and the number of technology market contracts in Hunan. This indicates that digital finance development and market environment optimization substantially contribute to strengthening the regional digital innovation environment.

(3) The evaluation results reveal that, from 2013 to 2023, the digital innovation environment scores of 29 provinces and municipalities exceeded their corresponding digital innovation investment scores. Only Guangdong Province recorded a higher digital innovation investment score than its environment score; however, Guangdong’s digital innovation environment also showed a consistent upward trend during the same period. These findings indicate a marked improvement in the digital innovation environment across all 30 provinces and municipalities throughout the study period. The ongoing optimization of the digital innovation environment is responsible for this improvement. As a result, innovation vitality has been greatly enhanced, regional digital innovation achievements have been more readily transferred and transformed, and RDIES systems have evolved toward greater stability and order.

(4) From the evolution trend in Figure 4, by comparing the six time points of 2013, 2015, 2017, 2019, 2021, and 2023, the dissipative evolution of RDIES systems in the sample regions generally follows a trajectory of “third quadrant → second quadrant → first quadrant,” indicating a progressive shift toward the state of high regional digital innovation investment and high regional digital innovation environment.

(5) The analysis reveals evident heterogeneity in the dissipative evolution trajectories of RDIES systems among the sample regions. Throughout the study period, Guangdong Province consistently led in digital innovation investment, with its evaluation values for investment remaining higher than those for the digital innovation environment. Nevertheless, over the study period, Guangdong Province never formed a dissipative structure, indicating that it is difficult to form a dissipative structure merely with high digital innovation investment. Between 2013 and 2023, the digital innovation environment in Beijing outperformed that in other provinces and cities. Comparative data shows that Guangdong’s investment in digital innovation is significantly higher than that of Beijing, but its digital innovation environment is slightly inferior to that of Beijing. Notably, the dissipation level in Beijing substantially exceeds that of Guangdong, suggesting that increasing digital innovation investment alone is insufficient to establish a dissipative structure. This suggests that, compared with investment, the digital innovation environment serves as a constraining factor, leading to lower dissipation levels in RDIES systems.

5. Discussion

5.1. Research Implications

The RDIES system, formed through the integration of digital innovation and innovation ecosystems, operates as a complex adaptive system guided by the principles of self-organization [46]. Adopting this approach, the study integrates ecological theory and complexity science, employing dissipative structure theory to analyze the evolutionary dynamics and features of the ecosystem from a symbiotic standpoint. Such an approach provides macro-level insights into the processes by which RDIES systems adapt to external environments through material and energy exchange. Furthermore, it offers essential theoretical support for optimizing regional digital innovation resource allocation and guiding policy development. The results suggest that RDIES systems meet the four essential characteristics of dissipative structures: openness, nonlinearity, disequilibrium, and fluctuations. Therefore, they can be appropriately analyzed using dissipative structure theory. Existing research has examined the construction of digital innovation ecosystems, their self-organizing features, and the composition of dissipative structures [47]. Unlike prior research confined to reviews or case studies, the empirical analysis in this study reveals a rising dissipation level in China’s RDIES systems between 2013 and 2023. The results further demonstrate that digital innovation resource input alone is insufficient to drive the formation of a dissipative structure. Achieving effective coordination alongside improvements in the digital innovation environment is essential. Enhancing the dissipation level of RDIES systems and fostering an innovation-driven economic transformation require simultaneously expanding investment in digital innovation resources and optimizing the digital innovation environment, with effective coordination between the two to promote system development and evolution. The study advances the literature by empirically examining the dissipative evolution of RDIES systems and by offering theoretical and methodological directions for future research.

Furthermore, a dual “global entropy–catastrophe progression” model is used to evaluate dynamically the dissipative evolution of China’s RDIES systems. The findings show that the two-dimensional framework of a “digital innovation investment-digital innovation environment” in the sample regions generally presents an evolutionary trajectory from the third quadrant to the second quadrant and then to the first quadrant. The evaluation values of digital innovation input and digital innovation environment both show an upward trend. RDIES systems display varying dissipative evolution patterns. Digital innovation investment and environmental development are strongest in the eastern region, moderate in the central region, and comparatively weaker in the northeastern and western regions. The observed pattern reflects the eastern region’s first-mover advantage in digital innovation, with strong digital infrastructure and ample financial and technological resources supporting the growth of its digital innovation ecosystem. In contrast, the development of digital innovation ecosystems in the central, western, and northeastern regions is constrained by inadequate digital infrastructure, limited resource mobility, and low allocation efficiency, aligning with the findings of Ma et al. [5].

5.2. Limitations and Future Research Directions

While this research empirically investigates the dissipative evolution of RDIES systems from a symbiotic perspective, certain limitations remain. First, due to objective constraints in data availability, statistics related to the digital industry are incomplete in official yearbooks. Although missing data were supplemented during preprocessing using methods such as moving averages, nearest-neighbor interpolation, and mean imputation to preserve the original characteristics and trends of the dataset, these procedures may nevertheless influence the robustness of the conclusions. Future studies could enhance the reliability of their findings through more comprehensive, high-quality data, multiple imputation methods, and bias testing.

Second, the factors influencing the digital innovation environment are diverse. Future studies could broaden the scope of analysis by incorporating additional elements such as intellectual property protection and data governance.

Finally, this research focused exclusively on the Chinese context. Future research could expand this analysis to the RDIES system of multiple countries within a unified framework, enabling comparative assessment of dissipative evolution and offering broader policy guidance.

6. Conclusions and Recommendations

6.1. Conclusions

This research analyzes the evolution of RDIES systems using the Brusselator translation of dissipative structure theory. Guided by symbiotic theory, a “digital innovation investment–digital innovation environment” evaluation index system is constructed, and the conditions for identifying dissipative structures are established based on the stability of evolutionary dynamics. The dual “global entropy–catastrophe progression” model is then employed to dynamically examine the evolutionary trajectory of the dissipative structure in RDIES systems. Using a dissipative structure determination model and empirical analysis of 30 Chinese provinces’ RDIES systems between 2013 and 2023, this study demonstrates that:

(1) The dynamic evolution of the RDIES system in the sample area satisfies the necessary conditions for the formation of a dissipative structure. The sample regions have not formed a dissipative structure from 2013 to 2023 and have not yet established a more orderly and higher-form RDIES system. In general, the eastern region’s digital innovation ecosystem exhibits a dissipation level above the national average. In the central region, the digital innovation ecosystem’s dissipation level has risen significantly, exceeding the national average since 2019. In contrast, the western and northeastern regions continue to perform below the national average.

(2) The evaluation values of digital innovation investment and digital innovation environment both showed an upward trend. Between 2013 and 2023, the digital innovation environment in the sample regions—including economic, policy, and market dimensions—has markedly improved, effectively stimulating regional digital innovation vitality, enhancing the efficiency of innovation outcome transformation, and advancing the evolution of the RDIES system toward a more orderly and stable state.

(3) By examining the six time points of 2013, 2015, 2017, 2019, 2021, and 2023, and employing a two-dimensional framework of “digital innovation investment–digital innovation environment,” the digital innovation ecosystem across the sample regions demonstrates an evolutionary trajectory from the third quadrant to the second quadrant and ultimately to the first quadrant, progressively advancing toward a high-level, balanced development.

6.2. Recommendations

Building on the above conclusions, the study offers the following suggestions to promote the dissipative evolution of RDIES systems: (1) Increase investment in digital innovation. First, regions are encouraged to prioritize diverse applications of digital technologies and advance the construction of new digital infrastructures, including IoT networks, blockchain systems, and data centers. Simultaneously, strengthening digital innovation platforms is essential, focusing on investment in research institutions and laboratories, development of open-source and algorithm platforms, and full utilization of emerging platform capabilities. Second, all regions should prioritize the enhancement of digital infrastructure by promoting the upgrading and expansion of optical fiber networks, optimizing the layout of 5G base stations, fostering the consumer Internet, and establishing big data research centers. Simultaneously, the digital and intelligent upgrading of existing infrastructure should be implemented. Third, all regions should focus on a digital innovation talent strategy, targeting critical areas like new-generation information technology and cultivating local digital innovation professionals. Optimize the policies for introducing digital talents and attract the aggregation of high-end digital talents.

(2) Improve the digital innovation environment. First, regions should enhance the digital economy by improving the innovation and entrepreneurship environment and reducing institutional costs. This includes improving digital innovation input–output efficiency, accelerating the transformation of innovation outcomes, and building channels that link digital innovation with production to enhance productivity. Second, create a supportive environment for digital finance and establish a multi-tiered, widely accessible, and sustainable digital inclusive financial system. Regions should employ blockchain, big data, and AI to develop a digital innovation financial ecosystem, maximizing the capacity of digital finance to connect and support collaboration among innovation actors. Third, the policy framework for the digital economy should be enhanced, emphasizing the promotion of data system innovation, the deepening of industrial digital transformation, and the acceleration of digital industry upgrading. By coordinating the allocation of digital resource elements, enhance the synergy of policies.

(3) In light of the pronounced disparities between digital innovation investment and the digital innovation environment, different regions should implement differentiated development strategies to facilitate the coordinated advancement of these two dimensions. The eastern region needs to develop national-level digital innovation platforms, steer the agglomeration of digital industries, capitalize on the “leading goose” effect of enterprises in clusters, and facilitate resource sharing and co-creation via strong innovation protection and market mechanisms, thereby strengthening digital industrialization and industrial digitalization and establishing a national digital innovation growth pole [48]. The central and western regions should actively engage in the “Eastern Digital, Western Computing” initiative, capitalize on policy incentives for digital technology, attract diversified investment for digital infrastructure, strengthen digital industry capabilities, and assume the relocation of high-end digital industries from the eastern region. Furthermore, regions should fully utilize their climatic and geographical advantages, and based on local characteristic industries, develop distinctive digital innovation application scenarios to further unlock the potential of regional digital innovation [28]. The Northeast region should promote market-driven data allocation, accelerate enterprise digital transformation [7], and establish a digital innovation closed loop from R&D to commercialization, while developing a consortium of key enterprises, universities, and research institutes to integrate technological innovation with industry.