IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0358392

W M Macek, D Wójcik

引用次数: 0

Coevolutionary game dynamics with local and global environmental feedbacks on spatially embedded networks. 空间嵌入网络中具有局部和全局环境反馈的协同进化博弈动力学。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0351862

Yi Zhong, Chuan Ding, Xiaojie Chen

{"title":"Coevolutionary game dynamics with local and global environmental feedbacks on spatially embedded networks.","authors":"Yi Zhong, Chuan Ding, Xiaojie Chen","doi":"10.1063/5.0351862","DOIUrl":"https://doi.org/10.1063/5.0351862","url":null,"abstract":"In recent years, the coevolutionary dynamics between game strategies and environmental states have attracted considerable attention. Most existing relevant studies focus on well-mixed populations or regular lattices and have yet to systematically investigate strategy-environment coevolutionary dynamics on complex spatial structures. In this work, we construct spatially embedded networks with three typical degree distributions (delta, Poisson, and power-law distributions), based on which we establish a multi-agent coevolutionary model with local and global environmental feedbacks. Using Monte Carlo simulations, we investigate the impacts of degree heterogeneity, average degree, and random connectivity on system dynamics. Simulation results show that the degree distribution significantly alters the system's dynamical behaviors. Among the three network topologies, homogeneous-degree networks are most conducive to dynamical stability. Moreover, average degree exerts a universal effect across all networks: cooperation level follows a unimodal trend, increasing first and then decreasing as average degree increases, with the maximum achieved at an intermediate average degree. This study explores how spatially embedded networks shape coevolutionary game dynamics and offers insights into the evolution of cooperation in complex adaptive systems.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 9","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148966991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The role of geometry in q-deformations. 几何在q-变形中的作用。

IF 3.3 2区数学

Chaos Pub Date : 2026-08-01 DOI: 10.1063/5.0333588

José S Cánovas, Houssem Eddine Rezgui

引用次数: 0

Erratum: "Optimal interaction functions realizing higher-order Kuramoto dynamics with arbitrary limit-cycle oscillators" [Chaos 36, 023120 (2026)]. 勘误：“实现具有任意极限环振子的高阶Kuramoto动力学的最优交互函数”[j]。

IF 3.3 2区数学

Chaos Pub Date : 2026-08-01 DOI: 10.1063/5.0352504

Norihisa Namura, Riccardo Muolo, Hiroya Nakao

引用次数: 0

Vertex-level diffusion scaling from resistance distance. 从阻力距离进行顶点级扩散缩放。

IF 3.3 2区数学

Chaos Pub Date : 2026-08-01 DOI: 10.1063/5.0338320

Chun-Xiao Nie

{"title":"Vertex-level diffusion scaling from resistance distance.","authors":"Chun-Xiao Nie","doi":"10.1063/5.0338320","DOIUrl":"https://doi.org/10.1063/5.0338320","url":null,"abstract":"The analysis of random walks on networks often relies on global quantities that average over nodes, thereby masking local differences in diffusion speed. This study introduces a vertex-level quantity Hi, defined as the finite-window fitted scaling exponent of the mean squared resistance distance ⟨Ωi2(t)⟩∼Cit2Hi from a given node i. We found nodes with Hi values below 0.5 (echo effect) and above 0.5 (catapult effect). The exponent is computed exactly via matrix powers of the transition matrix. We systematically evaluate Hi on several synthetic network families, generalized Sierpiński graphs, Newman-Watts small-world networks, and a custom grid-path-complete graph, and on two real-world networks (international E-road network and western U.S. power grid). We found nodes with Hi values less than 0.5 (subdiffusive regime) and greater than 0.5 (apparent superdiffusion) in both model networks and real-world networks. Analysis of model networks shows that when a node has an echo effect, its Hi value is less than 0.5, whereas when it has a catapult effect, its Hi value is greater than 0.5. In the two real networks, most nodes are in the subdiffusive regime and the overall heterogeneity of the local diffusion exponents is low, as indicated by Rényi indices of 0.0835 (E-road network) and 0.0555 (power grid). Comparisons with classical centrality measures indicate that Hi provides information not captured by those measures. The local diffusion exponent offers a vertex-level, dynamics-based tool for identifying structural bottlenecks and node roles, complementing global network characterizations.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 8","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148788896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Reinforcement-learning-based replicator-mutator dynamics for game-environment coevolution in public goods games. 基于强化学习的公共产品博弈中博弈-环境协同进化的复制-突变动力学。

IF 3.3 2区数学

Chaos Pub Date : 2026-08-01 DOI: 10.1063/5.0343966

Xinyu Liu, Linchao Pan, Chunying Ren, Bangxin Jiang, Changbing Tang

{"title":"Reinforcement-learning-based replicator-mutator dynamics for game-environment coevolution in public goods games.","authors":"Xinyu Liu, Linchao Pan, Chunying Ren, Bangxin Jiang, Changbing Tang","doi":"10.1063/5.0343966","DOIUrl":"10.1063/5.0343966","url":null,"abstract":"The reciprocal feedback between individual strategies and environmental states has received widespread attention in mathematical biology and ecology. However, existing game-environment feedback models typically focus on myopic payoff-driven adaptation, overlooking how individuals adjust their behavior based on long-term learning outcomes. In this paper, we derive a learning-induced mutation term from frequency-adjusted Q-learning with Boltzmann exploration to describe how long-term value learning shapes exploratory strategy adjustment. Based on this, we then embed the learning-induced mutation term into game-environment feedback dynamics, leading to reinforcement-learning-based replicator-mutator dynamics for public goods games. In the above coupled framework, the cooperation frequency affects the environmental state, while the environmental state reshapes the payoff difference and, hence, the strategy dynamics. More importantly, the derived mutation term is nonlinear and frequency-dependent, capturing exploratory strategy adjustments based on long-term value learning. Specifically, the learning-rate scale plays a crucial role in system dynamics, and appropriate learning-rate scales can help maintain positive cooperation and mitigate the tragedy of the commons. In addition, a low learning-rate scale may weaken the local damping around the interior equilibrium and lead to long-lived damped strategy-environment oscillations with reduced amplitude, providing insights into how learning-induced exploration regulates coevolutionary fluctuations.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 8","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148700830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Polynomial Lyapunov exponents: A practical scaling tool for weak instability in Rn. 多项式李雅普诺夫指数：Rn中弱不稳定性的实用标度工具。

IF 3.3 2区数学

Chaos Pub Date : 2026-08-01 DOI: 10.1063/5.0328618

N S Hoang

{"title":"Polynomial Lyapunov exponents: A practical scaling tool for weak instability in Rn.","authors":"N S Hoang","doi":"10.1063/5.0328618","DOIUrl":"https://doi.org/10.1063/5.0328618","url":null,"abstract":"Classical Lyapunov exponents characterize stability through exponential separation of nearby trajectories. However, many dynamical systems exhibit weak instability, in which perturbations grow subexponentially and the maximal Lyapunov exponent vanishes. In such cases, exponential diagnostics are unable to distinguish qualitatively different long-time behaviors. We introduce the polynomial Lyapunov exponent (PLE) as a scaling-based quantity that captures power-law separation of trajectories in systems where λ = 0. We establish basic properties of the PLE, including invariance under equivalent norms and a two-sided comparison principle that relates a limiting PLE to polynomial upper and lower bounds on perturbation growth. We also present a simple numerical estimator based on linear regression in logarithmic time and apply it to benchmark systems exhibiting weak instability, including nonnormal linear flows and marginally stable dynamics. These examples show that the PLE provides an interpretable and practical measure of polynomial growth rates in settings where classical Lyapunov exponents are inconclusive. The approach is tailored to polynomial scaling and is not intended to capture more general subexponential behavior. Numerical experiments demonstrate robustness with respect to perturbation magnitude and direction.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 8","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148711598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Core-periphery dynamics in market-conditioned financial networks: A conditional p-threshold mutual information approach. 市场条件下金融网络的核心-外围动态：条件p阈值互信息方法。

IF 3.3 2区数学

Chaos Pub Date : 2026-08-01 DOI: 10.1063/5.0320572

Kundan Mukhia, Imran Ansari, Salam Rabindrajit Luwang, Md Nurujjaman

{"title":"Core-periphery dynamics in market-conditioned financial networks: A conditional p-threshold mutual information approach.","authors":"Kundan Mukhia, Imran Ansari, Salam Rabindrajit Luwang, Md Nurujjaman","doi":"10.1063/5.0320572","DOIUrl":"https://doi.org/10.1063/5.0320572","url":null,"abstract":"This study investigates how financial market structure reorganizes during the COVID-19 crash using a conditional p-threshold mutual information (MI) based Minimum Spanning Tree (MST) network framework. We analyze nonlinear dependencies among the largest stocks from four economically diverse QUAD countries: the United States, Japan, Australia, and India. The crash period is identified using the Hellinger distance and further characterized by the Hilbert spectrum. A crash is defined when the Hellinger distance exceeds the threshold, enabling the segmentation of the data into pre-crash, crash, and post-crash periods. To isolate direct stock-level dependencies, the conditional p-threshold MI approach filters out common market effects and applies permutation-based significance testing. The resulting statistically validated dependencies are used to construct MST networks, allowing consistent comparison across market periods. The network analysis reveals common crisis-related dynamics across all markets. During the crash, networks become more integrated, with shorter path lengths and higher centrality, while algebraic connectivity declines, indicating increased structural fragility. A clear reorganization of the core-periphery structure is observed, with declining core concentration and increasing periphery fragility, supported by disassortative mixing that facilitates shock transmission. In the post-crash period, network topology shows partial and non-uniform recovery, suggesting persistent structural effects. This interpretation is further supported by an aftershock analysis based on the Gutenberg-Richter law, which indicates a higher relative frequency of large volatility events following the crash. The consistency of these findings across all four markets highlights the effectiveness of the conditional p-threshold MI framework for capturing nonlinear interdependencies and systemic vulnerability in financial markets.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 8","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148663446","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Adjustable soliton states via interaction-induced relative phase shifts in a Heisenberg ferromagnetic spin chain. 通过海森堡铁磁自旋链中相互作用诱导的相对相移来调节孤子态。

IF 3.3 2区数学

Chaos Pub Date : 2026-08-01 DOI: 10.1063/5.0339767

Yang Ren, Liang Duan, Xin-Wei Cao, Liang Guo

{"title":"Adjustable soliton states via interaction-induced relative phase shifts in a Heisenberg ferromagnetic spin chain.","authors":"Yang Ren, Liang Duan, Xin-Wei Cao, Liang Guo","doi":"10.1063/5.0339767","DOIUrl":"https://doi.org/10.1063/5.0339767","url":null,"abstract":"We investigate the interaction characteristics of solitons on a spin-wave background with various nonlinear magnetic excitations in a Heisenberg ferromagnetic spin chain with twisting interactions. We show that interactions with spatially periodic Akhmediev breathers generate an additional phase contribution, which reconstructs the relative phase between the soliton and the spin-wave background and consequently induces structural deformation and state transitions. In contrast, interactions with spatially non-periodic Kuznetsov-Ma breathers, and rogue waves do not modify the relative phase and therefore preserve the soliton state. An explicit analytical expression for the additional phase is derived, and its magnitude is found to depend on the initial relative phase of the soliton, the number of magnons carried by the soliton excitation, and the spatial periodicity of the breather. Based on these parameters, phase diagrams are constructed to characterize relative-phase-controlled soliton-state transitions. These findings reveal the role of interaction-induced additional phases in governing magnetic soliton-state transitions and may be relevant for future magnonic information-processing schemes.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 8","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148759021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Topology as a language for emergent organization in complex systems: Multiscale structure, higher-order interactions, and structural diagnostics. 拓扑作为复杂系统中紧急组织的语言：多尺度结构、高阶相互作用和结构诊断。

IF 3.3 2区数学

Chaos Pub Date : 2026-08-01 DOI: 10.1063/5.0337419

Mark M Bailey

{"title":"Topology as a language for emergent organization in complex systems: Multiscale structure, higher-order interactions, and structural diagnostics.","authors":"Mark M Bailey","doi":"10.1063/5.0337419","DOIUrl":"https://doi.org/10.1063/5.0337419","url":null,"abstract":"Complex systems are difficult to study not only because they are nonlinear, multiscale, and nonstationary, but because their scientifically relevant organization is often distributed across components, relations, and interaction orders. Topology provides a mathematical language for describing that organization through connectedness, recurrence, branching, closure, cavities, and persistence across scale. This review synthesizes persistent homology, Mapper, simplicial complexes, hypergraphs, and relation-level operator methods through a unified workflow from empirical data to representation, topological construction, output, and scientific interpretation. Across nonlinear dynamics, finance, neuroscience, biology, ecology, materials, and engineered systems, topological and topology-inspired methods make state-space organization, collective constraints, and structural reorganization available as observables that can be integrated with statistics, dynamics, mechanistic models, and machine learning. The review distinguishes the claim that a representation makes structure visible from the stronger claim that it improves detection or prediction, and it summarizes comparative evidence where such benchmarks exist. Prospective early-warning evidence remains uneven, but several studies demonstrate useful structural diagnostics, data-efficient classification, anomaly detection, and reductions in false alarms. The central conclusion is that topology is most valuable when representation is treated as a scientific hypothesis and topological descriptions are connected to domain-matched inference and mechanism.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 8","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148825655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

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