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Mathematics
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Dynamic Analysis and Decision-Making in Complex Networks, 2nd Edition
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Dynamic Analysis and Decision-Making in Complex Networks, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 31 March 2027 | Viewed by 1223

Special Issue Editor

Dr. Dun Han

E-Mail Website
Guest Editor
School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, China
Interests: complex networks and communication dynamics; intelligent decision-making and nonlinear complex systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue focuses on dynamic behaviors and decision-making mechanisms within complex networks, which are fundamental to understanding and managing real-world systems such as social networks, transportation systems, power grids, and biological networks. We invite high-quality contributions that explore theoretical models, computational methods, and applications involving dynamic processes—such as diffusion, synchronization, control, or game–theoretic interactions—in evolving or multilayer network structures. Topics of interest include, but are not limited to, the following: networked decision dynamics, emergent behaviors, stability analysis, optimal control, and data-driven modeling approaches. By bringing together cutting-edge research from mathematics, systems science, and applied domains, this Special Issue aims to promote interdisciplinary advancements in the analysis, prediction, and design of intelligent and resilient networked systems.

Dr. Dun Han
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • complex networks
  • dynamic systems
  • network decision-making
  • evolutionary game theory
  • diffusion and propagation
  • multi-agent systems
  • stability and control network optimization
  • multilayer networks
  • data-driven modeling

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Related Special Issue

Published Papers (3 papers)

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Research

19 pages, 1044 KB  
Article
Algebraic Topology Modeling and Game Decision Optimization for Multilayer Complex Network Dynamics
by Yandong Yuan
Mathematics 2026, 14(11), 1817; https://doi.org/10.3390/math14111817 - 24 May 2026
Viewed by 177
Abstract
Modeling and controlling multilayer complex network dynamics is challenging under coexisting crosslayer interactions, higher-order couplings, and decentralized strategic decisions. Most existing schemes focus on graph-based pairwise structures and overlook topological cavities, mesoscale loops, and layered self-interested actions. This paper presents TopoGame-MND, an algebraic-topological [...] Read more.
Modeling and controlling multilayer complex network dynamics is challenging under coexisting crosslayer interactions, higher-order couplings, and decentralized strategic decisions. Most existing schemes focus on graph-based pairwise structures and overlook topological cavities, mesoscale loops, and layered self-interested actions. This paper presents TopoGame-MND, an algebraic-topological and game-theoretic framework for multilayer network dynamics. We first build a filtration-driven simplicial lifting to unify pairwise and higher-order interactions into a weighted multilayer simplicial complex. A topological state operator using generalized Hodge Laplacians and persistent homology is then constructed to characterize cross-scale diffusion, circulation, and structural inconsistency. A distributed potential-game mechanism is developed with a topology-aware utility, followed by a proximal mirror-best-response algorithm with consensus correction. We prove Nash equilibrium existence and uniqueness, global potential monotone descent, linear convergence, computational complexity, and input-to-state robustness. Simulations on multiplex and interdependent networks validate that TopoGame-MND outperforms baselines in regulation speed, oscillation energy, failure resilience, and robustness, providing a unified way to connect higher-order topology and distributed decision optimization. Full article
(This article belongs to the Special Issue Dynamic Analysis and Decision-Making in Complex Networks, 2nd Edition)
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24 pages, 1075 KB  
Article
The Spatio-Temporal Differentiation and Convergence Characteristics of the Coordinated Development of Digitalization and Greening in China
by Peipei Zhang and Yusen Luo
Mathematics 2026, 14(9), 1574; https://doi.org/10.3390/math14091574 - 6 May 2026
Viewed by 255
Abstract
The synergistic development of digitalization and greening is an important lever for China to accelerate the formation of new quality productive forces. This study adopted the global entropy method and coupling coordination degree model to measure the level of coordinated development between digitalization [...] Read more.
The synergistic development of digitalization and greening is an important lever for China to accelerate the formation of new quality productive forces. This study adopted the global entropy method and coupling coordination degree model to measure the level of coordinated development between digitalization and greening with the panel data of Chinese cities from 2011 to 2022. Spatio-temporal evolution characteristics were explored through kernel density estimation, the Dagum Gini coefficient, and spatial autocorrelation methods. This study further tested the convergence characteristics of coordinated development through a two-way fixed effect model and spatial econometric model. The results show the following: (1) The overall level of coordinated development of digitalization and greening in China is on the rise, with the development level in the eastern region being significantly higher than that in the central and western regions. The degree of differentiation in coordinated development shows a trend of decreasing first and then increasing, mainly due to regional differences. (2) The level of coordinated development between digitalization and greening in China shows a significant positive spatial autocorrelation feature, with a clustering pattern dominated by “low–low” clustering. (3) It is found that the coordinated development of digitalization and greening in China has significant characteristics of σ convergence, spatial β convergence and club convergence. Full article
(This article belongs to the Special Issue Dynamic Analysis and Decision-Making in Complex Networks, 2nd Edition)
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20 pages, 6100 KB  
Article
Complex Dynamics of a Supply–Demand–Price Network Model Incorporating a Marginal Feedback Mechanism
by Dingyue Wang, She Han and Mei Sun
Mathematics 2026, 14(8), 1337; https://doi.org/10.3390/math14081337 - 16 Apr 2026
Viewed by 274
Abstract
In this paper, a supply–demand–price network model incorporating a marginal feedback mechanism is proposed to characterize the evolution of market prices. Unlike classical supply–demand models, the marginal effect of excess demand, defined as the rate of change in excess demand, is explicitly introduced [...] Read more.
In this paper, a supply–demand–price network model incorporating a marginal feedback mechanism is proposed to characterize the evolution of market prices. Unlike classical supply–demand models, the marginal effect of excess demand, defined as the rate of change in excess demand, is explicitly introduced into the price adjustment process. As the coefficient of the marginal feedback term varies, the system exhibits rich and complex nonlinear dynamics. In particular, the model gives rise to a centrally symmetric double-wing chaotic attractor, as well as a pair of coexisting single-wing chaotic attractors. The transition routes among different dynamical regimes are systematically analyzed using phase portraits, bifurcation diagrams, and Lyapunov exponents. Furthermore, multistability phenomena are observed, including the coexistence of equilibrium points, limit cycles, and chaotic attractors. The corresponding basins of attraction are illustrated to reveal their intricate and interwoven structures. In addition, the emergence of endogenous chaos is investigated through both theoretical analysis and numerical simulations. Finally, the consistency between the model dynamics and real market data provides empirical evidence supporting the validity and applicability of the proposed framework. Full article
(This article belongs to the Special Issue Dynamic Analysis and Decision-Making in Complex Networks, 2nd Edition)
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