Search Results (45)

Mathematical modeling plays a crucial role in supporting decision-making across a wide range of scientific disciplines. These models often involve multiple parameters, the estimation of which is critical to assessing their reliability and predictive power. Recent advancements in artificial intelligence have made it possible to efficiently estimate such parameters with high accuracy. In this study, we focus on modeling the dynamics of cryptocurrency market shares by employing a Lotka–Volterra system. We introduce a methodology based on a deep neural network (DNN) to estimate the parameters of the Lotka–Volterra model, which are subsequently used to numerically solve the system using a fourth-order Runge–Kutta method. The proposed approach, when applied to real-world market share data for Bitcoin, Ethereum, and alternative cryptocurrencies, demonstrates excellent alignment with empirical observations. Our method achieves RMSEs of 0.0687 (BTC), 0.0268 (ETH), and 0.0558 (ALTs)—an over 50% reduction in error relative to ARIMA(2,1,2) and over 25% relative to a standard NN–ODE model—thereby underscoring its effectiveness for cryptocurrency-market forecasting. The entire framework, including neural network training and Runge–Kutta integration, was implemented in MATLAB R2024a (version 24.1). Full article

In this integrative review paper, we explore the parallels between the physical models of gyrotrons and some equations used in diverse and broad scientific fields. These include Adler’s famous equation, Van der Pol equation, the Lotka–Volterra equations and the Kuramoto model. The paper is written in the form of a pedagogical discourse and aims to provide additional insights into gyrotron physics through analogies and parallels to theoretical approaches used in other fields of research. For the first time, reachability analysis is used in the context of gyrotron physics as a modern tool for understanding the behavior of nonlinear dynamical systems. Full article

Regulating lamprey populations is crucial for maintaining ecological equilibrium. However, the unique sex determination process of lampreys is constrained by multiple factors, complicating intuitive analysis of population dynamics and their impact on the natural environment. This study employed a two-species competition mechanism to elucidate the factors influencing sex ratios and their mechanistic effects on lamprey population size. Using the Lotka–Volterra equations, we investigated how sex ratios affect trophic levels both upstream and downstream of lampreys in the food web. A logistic population growth model was applied to assess the impact of sex ratio variations on symbiotic parasitic species, while the Analytic Hierarchy Process (AHP) was utilized to explore the dynamic relationship between sex ratio changes and ecosystem stability. To validate model efficacy, we manipulated temperature and food availability under controlled disturbance conditions, analyzing temporal variations in lamprey population size across different disturbance intensities to evaluate model sensitivity. The findings indicate that the variable sex ratio’s benefit is in facilitating the lampreys’ population’s enhanced adaptation to environmental shifts. The coexisting species exhibit a similar pattern of population alteration as the lampreys, albeit with a minor delay. A definitive link between the quantity of lampreys and the parasitic species is absent. A male ratio of 0.6 optimally contributes to the ecosystem’s equilibrium. Over time, the configuration of our model’s parameters proves to be sensible. This research provides robust theoretical support for developing scientific strategies to regulate lamprey populations. Full article

With the shift of the global innovation model from traditional closed-loop to open ecosystems, knowledge sharing and collaborative cooperation among firms have become key to obtaining sustainable competitive advantages. However, existing studies mostly focus on the static structure, and there is an insufficient exploration of the dynamic evolutionary mechanism and multi-party game strategies. In this paper, a two-dimensional analysis framework integrating the evolutionary game and the Lotka–Volterra model is constructed to explore the behavioral and strategic evolution of core enterprises, SMEs and the government in the innovation ecosystem. Through theoretical modeling and numerical simulation, the effects of different variables on system stability are revealed. It is found that a moderately balanced benefit allocation can stimulate two-way knowledge sharing, while an over- or under-allocation ratio will inhibit the synergy efficiency of the system; a moderate difference in the knowledge stock can promote knowledge complementarity, but an over-concentration will lead to the monopoly and closure of the system; and the government subsidy needs to accurately match the cost of the openness of the enterprises with the potential benefits to the society, so as to avoid the incentive from being unused. Accordingly, it is suggested to optimize the competition structure among enterprises through the dynamic benefit distribution mechanism, knowledge sharing platform construction and classification subsidy policy, promote the evolution of the innovation ecosystem to a balanced state of mutual benefit and symbiosis, and provide theoretical basis and practical inspiration for the governance of the open innovation ecosystem. Full article

This study investigates a modified Lotka–Volterra commensalism system that incorporates the weak Allee effect in prey and symmetric (equal harvesting effort for both species) non-selective harvesting, addressing a critical gap in ecological modeling. Unlike previous work, we rigorously examine how the interaction between the Allee effect and harvesting disrupts system stability, giving rise to novel bifurcation phenomena and population collapse thresholds. Using eigenvalue analysis and the Dulac–Bendixson criterion, we derive sufficient conditions for the existence and stability of equilibria. We find that harvesting destabilizes the system by inducing two saddle-node bifurcations. Notably, prey abundance can increase with greater Allee intensity under controlled harvesting—a rare and counterintuitive ecological outcome. Moreover, exceeding a critical harvesting threshold drives both species to extinction, while controlled harvesting allows sustainable coexistence. Numerical simulations support these analytical findings and identify critical parameter ranges for species coexistence. These results contribute to theoretical ecology and offer insights for designing sustainable harvesting strategies that balance exploitation with conservation. Full article

Addressing the dual challenges of agricultural productivity and ecological sustainability, this study develops an integrated framework combining Lotka–Volterra dynamics, Monte Carlo simulation, and multi-objective optimisation to quantify agroecosystem responses under anthropogenic interventions. Key innovations include the incorporation of carbon sequestration dynamics and low-carbon agricultural practices into ecological–economic trade-off analysis. Our findings demonstrate the following: (1) Seasonal carbon fertilisation effects enhance producer growth by up to 30%, while energy recycling from consumer mortality offsets 22% of pesticide-induced carbon emissions. (2) The strategic introduction of dual-function species synergistically improves carbon sink capacity by 18–25% through enhanced producer efficiency and reduced chemical reliance. (3) Multi-objective optimisation reveals that integrated pest management coupled with organic amendments achieves a 51.2% net benefit improvement, while reducing agrochemical carbon footprints by 40–55%. The proposed framework bridges critical gaps in sustainable agriculture by simultaneously addressing yield stability, biodiversity conservation, and climate mitigation imperatives. This work advances the dynamic modelling of agroecosystems through probabilistic risk assessment and carbon-aware decision-making, providing actionable pathways for low-carbon agricultural intensification. Full article

High-tech industries are of strategic importance to the national economy, and Beijing has been designated as a science and technology innovation center by the State Council. Accurate analysis of its added value is crucial for technological development. While recent data enhance prediction accuracy, its limited volume poses challenges. The cumulative grey Lotka–Volterra model and grey differential dynamic multivariate model address this by leveraging short-term data effectively. This study applies these two models to analyze influencing factors and predict Beijing’s high-tech industry growth. Results show a competitive relationship with four systems, lacking synergy. In the next five years, a mutually beneficial trend is expected. The Mean Absolute Percentage Error (MAPE) remains within 10%, confirming the model’s reliability. Full article

This study investigates the competitive and cooperative relationships within urban agglomerations, specifically focusing on the Guangdong–Hong Kong–Macao Greater Bay Area (GBA). Using the Lotka–Volterra model from ecology, the research aims to analyse and predict the dynamic relationships among cities in this area. The purpose is to understand how competition and cooperation influence regional integration, and their complex economic connections. This paper employs both qualitative and quantitative methods, including time-series analysis and the application of the Lotka–Volterra model, to evaluate economic interactions and the roles of various cities or regions within the GBA. The study reveals that mutualistic, competitive, predatory, commensal, and parasitic relationships coexist among them, with core cities such as Shenzhen, Guangzhou, Hong Kong, and Macao assuming pivotal roles in shaping the overall dynamics. The findings highlight the importance of functional division, regional cooperation, and innovative collaboration to enhance sustainable development. Policy recommendations are provided to foster a balanced and integrated growth model, emphasizing inter-city cooperation, resource sharing, and avoidance of industrial homogeneity. Full article

A novel time delay Lotka–Volterra (TDLV) model was developed by extending the concept of time delay from integer order to fractional order. The TDLV model was constructed to simulate the dynamics of aboveground biomass per individual of three dominant herbaceous plant species (Leymus chinensis, Agropyron cristatum, and Stipa grandis) in the typical grasslands of Inner Mongolia. Comparative analysis indicated that the TDLV model outperforms candidate models, such as Logistic, GM(1,1), GM(1,N), DGM(2,1), and Lotka–Volterra model, in terms of all fitting criteria. The results demonstrate that interspecies competition exhibits clear feedback and suppression effects, with Leymus chinensis playing a central role in regulating community dynamics. The system is locally stable and eventually converges to an equilibrium point, though Stipa grandis maintains relatively low biomass, requiring further monitoring. Time delays are prevalent in the system, influencing dynamic processes and causing damping oscillations as populations approach equilibrium. Full article

We investigate the multidimensional stability of planar traveling waves in competitive–cooperative Lotka–Volterra system of three species in n-dimensional space. For planar traveling waves with speed $c>c^{*}$, we establish their exponential stability in $L^{\infty }\left({\mathbb{R}}^n\right)$, which is expressed as $t^{-\frac{n}{2}}{\mathrm{e}}^{-{\epsilon }_{\tau }\sigma t}$, where $\sigma >0$ is a constant and ${\epsilon }_{\tau }\in (0,1)$ depends on the time delay $\tau >0$ as a decreasing function ${\epsilon }_{\tau }=\epsilon \left(\tau \right)$. The time delay is shown to significantly reduce the decay rate of the solution. Additionally, for planar traveling waves with speed $c=c^{*}$, we demonstrate their algebraic stability in the form $t^{-\frac{n}{2}}$. Our analysis employs the Fourier transform and a weighted energy method with a carefully chosen weight function. Full article

The aim of this study was to compare the succession of natural microbiota in pork held under refrigerated storage for up to 10 days after dielectric barrier discharge (DBD) plasma treatment. Two methods were used to assess the impact of DBD on microorganisms. Firstly, traditional selective media (SM) were employed to detect the bactericidal effects of DBD on Pseudomonas spp., Enterobacteriaceae, Lactic acid bacteria (LAB), and Brochothrix thermosphacta. Secondly, the thin agar layer (TAL) method was used to further evaluate the bactericidal effects of DBD. In addition, the Baranyi and Roberts model was applied to explore the kinetic parameters of Pseudomonas spp., Enterobacteriaceae, LAB, and B. thermosphacta during storage. Finally, the modified Lotka–Volterra model was used to describe the interactions between each microorganism. The study found that when using traditional selective media (SM), 85 kV DBD had a significant bactericidal effect on Pseudomonas spp., Enterobacteriaceae, LAB, and Brochothrix thermosphacta. However, when using the thin agar layer (TAL) method, the results suggested that DBD had no significant bactericidal effect, suggesting that DBD caused sublethal damage to the natural microorganisms on pork. Analysis with the Baranyi and Roberts model showed that DBD treatment significantly extended the lag phase of these four types of microorganisms and significantly reduced the μ_max of all microorganisms except LAB. The analysis results of the modified Lotka–Volterra model showed that LAB had a greater impact on Pseudomonas spp., Enterobacteriaceae, and B. thermosphacta (a₂₁ > a₁₂). In conclusion, DBD treatment was shown to have a significant sublethal bactericidal effect that impacted both the count and composition of natural microorganisms found on pork. Full article

Mathematical models are designed to assist decision-making processes across various scientific fields. These models typically contain numerous parameters, the values’ estimation of which often comes under analysis when evaluating the strength of these models as management tools. Advanced artificial intelligence software has proven to be highly effective in estimating these parameters. In this research work, we use the Lotka–Volterra model to describe the dynamics of a telecommunication sector in Greece, and then we propose a methodology that employs a feed-forward neural network (NN). The NN is used to estimate the parameter’s values of the Lotka–Volterra system, which are later applied to solve the system using a fourth-algebraic-order Runge–Kutta method. The application of the proposed architecture to the specific case study reveals that the model fits well to the experiential data. Furthermore, the results of our method surpassed the other three methods used for comparison, demonstrating its higher accuracy and effectiveness. The implementation of the proposed feed-forward neural network and the fourth-algebraic-order Runge–Kutta method was accomplished using MATLAB. Full article

There is an interdependent symbiotic relationship between humans and water; scientific and effective assessment of the human–water symbiosis relationship is of great significance for the promotion of sustainable development. This study developed a novel framework of the human–water symbiosis relationship under an integrated perspective, which included theoretical interpretation, quantitative assessment, pattern discrimination, and an attribution analysis. Based on the symbiosis theory, the theoretical analysis of the human–water relationship was carried out to analyze the three basic elements of the human–water system, and then the evaluation index system of the human–water symbiosis system was constructed to quantitatively assess the development level of the human system and the water system. The Lotka–Volterra model was used to identify the symbiotic pattern, and the human–water symbiosis index was calculated to characterize the health state of the human–water symbiosis system. The main influencing factors of the human–water symbiosis system were further identified through an attribution analysis. Finally, a case study was carried out with 18 cities in Henan Province. Results reveal that (a) the proposed method can effectively realize the quantitative characterization of the human–water symbiosis relationship, with good applicability and obvious advantages; (b) the human–water symbiosis pattern of cities in Henan Province is dominated by the “human system parasitizes water system (H⁺W⁻)” pattern, and more attention should be paid to the water system in the subsequent development of it; and (c) the main factors influencing the human system, the water system, and the human–water symbiosis system are the research and development (R&D) personnel equivalent full-time (H7), per capita water resources (W1), and proportion of water conservancy and ecological water conservancy construction investment (W6), respectively. The findings can provide theoretical and methodological support for the study of the human–water symbiosis relationship and sustainable development in other regions. Full article

The species of the adaptive male–female sex ratio has different effects on the bio-community. This paper is aimed at figuring out these effects through mechanism analysis and Ordinary Differential Equation (ODE). Hence, the ODE environmental model is created by combining the Lotka–Volterra model, the interspecific model, and other external factors. The stability is used to characterize these effects. According to this model, effects on bio-community stability under different male–female sex ratios are roughly observed. By innovatively considering different living environments during the species’ lifecycle, the ODE environmental model is optimized, and the effects of different male–female sex ratios on the bio-community are further analyzed by phase-track maps and relative standard deviation. It is found that there are different findings and features in resource-rich and resource-scarce living environments during the lifecycle. Meanwhile, bio-communities in these two types of environments are in a stable state based on different male–female sex ratios. Based on these findings, directive opinions can be used to manage and help relevant bio-communities. Full article

In this paper, a class of two-delay differential equations with coefficient-dependent delay is studied. The distribution of the roots of the eigenequation is discussed, and conditions for the stability of the internal equilibrium and the existence of Hopf bifurcation are obtained. Additionally, using the normal form method and the central manifold theory, the bifurcation direction and the stability for the periodic solution of Hopf bifurcation are calculated. Finally, the correctness of the theory is verified by numerical simulation. Full article