Pub Date : 2026-10-27DOI: 10.1016/j.chaos.2026.119372
Junen Jia, Pengquan Zhang
Neural electrical activity depends on transmembrane ionic currents mediated by ion channels, while coupling between neurons further regulates collective firing rhythms and synchronization states. To investigate the effects of ion-channel shunting mechanisms and different coupling schemes on the dynamical and energy characteristics of neurons and their networks, we construct capacitive-shunting and inductive-shunting bimembrane memristive neural circuits and analyze their dynamical and energy characteristics. The results show that both the membrane capacitance ratio and periodic stimulation can induce transitions between firing modes and alter the neural energy level. Noise of an appropriate intensity introduced through the ion-channel branch can induce stochastic resonance, accompanied by a pronounced energy response. On this basis, magnetic flux-controlled memristors (MFCM) with identical parameters and initial states are used to connect the two types of neurons, with only the coupling location varied, thereby constructing membrane-coupled and ion-channel-coupled systems, respectively. The results reveal pronounced differences between the two coupling schemes in terms of dynamical behavior, synchronization, and energy characteristics. Membrane coupling generally promotes synchronization, whereas ion-channel coupling exhibits stronger state dependence and can substantially reorganize internal current transmission and energy exchange. These findings indicate that the coupling location is an important structural factor in regulating synchronization and energy exchange in neural networks. This study provides a theoretical reference for the design and regulation of coupling structures in neural networks.
{"title":"Membrane coupling and ion-channel coupling between heterogeneous bimembrane memristive neurons: Dynamics, synchronization, and energy characteristics","authors":"Junen Jia, Pengquan Zhang","doi":"10.1016/j.chaos.2026.119372","DOIUrl":"https://doi.org/10.1016/j.chaos.2026.119372","url":null,"abstract":"Neural electrical activity depends on transmembrane ionic currents mediated by ion channels, while coupling between neurons further regulates collective firing rhythms and synchronization states. To investigate the effects of ion-channel shunting mechanisms and different coupling schemes on the dynamical and energy characteristics of neurons and their networks, we construct capacitive-shunting and inductive-shunting bimembrane memristive neural circuits and analyze their dynamical and energy characteristics. The results show that both the membrane capacitance ratio and periodic stimulation can induce transitions between firing modes and alter the neural energy level. Noise of an appropriate intensity introduced through the ion-channel branch can induce stochastic resonance, accompanied by a pronounced energy response. On this basis, magnetic flux-controlled memristors (MFCM) with identical parameters and initial states are used to connect the two types of neurons, with only the coupling location varied, thereby constructing membrane-coupled and ion-channel-coupled systems, respectively. The results reveal pronounced differences between the two coupling schemes in terms of dynamical behavior, synchronization, and energy characteristics. Membrane coupling generally promotes synchronization, whereas ion-channel coupling exhibits stronger state dependence and can substantially reorganize internal current transmission and energy exchange. These findings indicate that the coupling location is an important structural factor in regulating synchronization and energy exchange in neural networks. This study provides a theoretical reference for the design and regulation of coupling structures in neural networks.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"29 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149274895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-27DOI: 10.1016/j.chaos.2026.119386
Wentao Wang, Xiaoli Li, Jun Tian
Cooperative missions in obstacle-dense mountainous environments pose severe safety challenges for Unmanned Aerial Vehicle (UAV) swarms. This study formulates multi-UAV dynamic trajectory planning as an optimization problem, utilizing a comprehensive cost model that encapsulates energy consumption, terrain and dynamic threat avoidance, and inter-UAV safety. To solve this highly constrained model, a Reinforcement Learning-integrated Multi-strategy Sine Cosine Algorithm (RLMSCA) is proposed to overcome the limitations of standard metaheuristics. Specifically, an elite pool t-distribution mutation actively maintains population diversity, a Gaussian fusion search ensures smooth phase transitions, and adaptive neighborhood quadratic interpolation provides local path refinement. Crucially, an embedded tabular reinforcement mechanism updates candidate-indexed operator preferences from iterative fitness-improvement feedback, enabling adaptive operator selection rather than relying on a fixed phase-transition schedule. Extensive CEC2017 benchmark evaluations demonstrate strong overall optimization performance, with RLMSCA achieving the best mean result on 18 of the 29 tested functions. Furthermore, three-dimensional flight simulations across six mountainous scenarios show that RLMSCA obtains the best overall Friedman rank and the lowest mean objective cost in five scenarios, demonstrating strong aggregate performance in cooperative UAV swarm trajectory planning.
{"title":"Cooperative path planning for UAV swarms in dynamic mountainous terrain using a reinforcement learning-guided sine cosine algorithm","authors":"Wentao Wang, Xiaoli Li, Jun Tian","doi":"10.1016/j.chaos.2026.119386","DOIUrl":"https://doi.org/10.1016/j.chaos.2026.119386","url":null,"abstract":"Cooperative missions in obstacle-dense mountainous environments pose severe safety challenges for Unmanned Aerial Vehicle (UAV) swarms. This study formulates multi-UAV dynamic trajectory planning as an optimization problem, utilizing a comprehensive cost model that encapsulates energy consumption, terrain and dynamic threat avoidance, and inter-UAV safety. To solve this highly constrained model, a Reinforcement Learning-integrated Multi-strategy Sine Cosine Algorithm (RLMSCA) is proposed to overcome the limitations of standard metaheuristics. Specifically, an elite pool t-distribution mutation actively maintains population diversity, a Gaussian fusion search ensures smooth phase transitions, and adaptive neighborhood quadratic interpolation provides local path refinement. Crucially, an embedded tabular reinforcement mechanism updates candidate-indexed operator preferences from iterative fitness-improvement feedback, enabling adaptive operator selection rather than relying on a fixed phase-transition schedule. Extensive CEC2017 benchmark evaluations demonstrate strong overall optimization performance, with RLMSCA achieving the best mean result on 18 of the 29 tested functions. Furthermore, three-dimensional flight simulations across six mountainous scenarios show that RLMSCA obtains the best overall Friedman rank and the lowest mean objective cost in five scenarios, demonstrating strong aggregate performance in cooperative UAV swarm trajectory planning.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"5 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149274891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-27DOI: 10.1016/j.chaos.2026.119381
Heng Song, Junhao Zhu, Chunbiao Li
Macroscopic instability in resource-constrained multi-agent systems poses a critical challenge for distributed AI. Contrary to attributing such volatility to suboptimal learning, we reveal that deterministic chaos is an endogenous topological property driven by discontinuous hard-threshold interaction protocols. Formulating a Discrete-Time Dynamical System (DTDS), we analytically prove the absence of stable equilibria; system trajectories are inevitably captured by an attracting heteroclinic-like network, quantitatively confirmed by positive finite-time Lyapunov exponents. Crucially, phase-space projections uncover “chaotic locus migration”, demonstrating that altering deterministic interaction protocols merely shifts the strange attractor across different agent ranks rather than resolving the systemic instability. To eliminate this instability, we propose a stochastic smoothing mechanism. The resulting multiplicative stochastic perturbation restores the continuity of the expected update mapping, for which we prove the existence of at least one fixed point. This topological regularization acts as an endogenous thermostat, balancing competing dynamical tendencies. Extensive simulations confirm that this targeted stochasticity induces a total attractor collapse, enabling the collective to escape the “deterministic trap” and achieve significant asymptotic gains in global stabilization and system throughput. This work provides a mechanistic approach to transforming endogenous chaos into robust probabilistic order in competitive systems.
{"title":"Chaos in resource-constrained multi-agent system and its stabilization","authors":"Heng Song, Junhao Zhu, Chunbiao Li","doi":"10.1016/j.chaos.2026.119381","DOIUrl":"https://doi.org/10.1016/j.chaos.2026.119381","url":null,"abstract":"Macroscopic instability in resource-constrained multi-agent systems poses a critical challenge for distributed AI. Contrary to attributing such volatility to suboptimal learning, we reveal that deterministic chaos is an endogenous topological property driven by discontinuous hard-threshold interaction protocols. Formulating a Discrete-Time Dynamical System (DTDS), we analytically prove the absence of stable equilibria; system trajectories are inevitably captured by an attracting heteroclinic-like network, quantitatively confirmed by positive finite-time Lyapunov exponents. Crucially, phase-space projections uncover “chaotic locus migration”, demonstrating that altering deterministic interaction protocols merely shifts the strange attractor across different agent ranks rather than resolving the systemic instability. To eliminate this instability, we propose a stochastic smoothing mechanism. The resulting multiplicative stochastic perturbation restores the continuity of the expected update mapping, for which we prove the existence of at least one fixed point. This topological regularization acts as an endogenous thermostat, balancing competing dynamical tendencies. Extensive simulations confirm that this targeted stochasticity induces a total attractor collapse, enabling the collective to escape the “deterministic trap” and achieve significant asymptotic gains in global stabilization and system throughput. This work provides a mechanistic approach to transforming endogenous chaos into robust probabilistic order in competitive systems.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"6 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149274900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-27DOI: 10.1016/j.chaos.2026.119374
Jiachen Feng, Wenxuan Xie, Zhixian Lv, Sajjad-ur Rehman, Yibao Li
We present a surrogate modeling framework for quasicrystal phase-field dynamics governed by the Lifshitz–Petrich free energy functional. The framework couples a β-variational autoencoder with a Transformer-based temporal predictor operating in the learned latent space. The β-VAE compresses high-dimensional phase fields into compact latent representations using a composite reconstruction loss, enabling an efficient reduced-order description of evolving quasicrystalline microstructures. The Transformer is then adopted to model the autoregressive temporal evolution of the encoded phase-field dynamics in the latent space. In addition, free-energy information is incorporated into the attention mechanism to provide a physics-informed guidance for temporal prediction. To further address long-horizon error accumulation, an Ensemble Kalman Filter is embedded in the latent space to assimilate observational information and correct autoregressive predictions. The proposed framework provides a unified latent-space modeling strategy that integrates representation learning, temporal prediction, physics-informed modeling, and data assimilation for surrogate modeling of quasicrystal phase-field dynamics.
{"title":"A latent-space surrogate modeling and data assimilation framework for quasicrystal phase-field dynamics","authors":"Jiachen Feng, Wenxuan Xie, Zhixian Lv, Sajjad-ur Rehman, Yibao Li","doi":"10.1016/j.chaos.2026.119374","DOIUrl":"https://doi.org/10.1016/j.chaos.2026.119374","url":null,"abstract":"We present a surrogate modeling framework for quasicrystal phase-field dynamics governed by the Lifshitz–Petrich free energy functional. The framework couples a <mml:math altimg=\"si64.svg\" display=\"inline\"><mml:mi>β</mml:mi></mml:math>-variational autoencoder with a Transformer-based temporal predictor operating in the learned latent space. The <mml:math altimg=\"si64.svg\" display=\"inline\"><mml:mi>β</mml:mi></mml:math>-VAE compresses high-dimensional phase fields into compact latent representations using a composite reconstruction loss, enabling an efficient reduced-order description of evolving quasicrystalline microstructures. The Transformer is then adopted to model the autoregressive temporal evolution of the encoded phase-field dynamics in the latent space. In addition, free-energy information is incorporated into the attention mechanism to provide a physics-informed guidance for temporal prediction. To further address long-horizon error accumulation, an Ensemble Kalman Filter is embedded in the latent space to assimilate observational information and correct autoregressive predictions. The proposed framework provides a unified latent-space modeling strategy that integrates representation learning, temporal prediction, physics-informed modeling, and data assimilation for surrogate modeling of quasicrystal phase-field dynamics.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"6 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149274892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-27DOI: 10.1016/j.chaos.2026.119356
Kongyun Huang, Changjing Zhou, Xiuyuan Xiong, Xudong Yang, Yingzhe Song, Kai Xu, Johann H. Martínez, Miguel-Ángel Gómez-Ruano, Javier M. Buldú
Mean-field percolation theory offers analytical predictions for network robustness, but its empirical validity for finite, directed, spatial networks depends on how those networks are represented. We analyse directed bond percolation in 4560 team-match pitch-player passing networks from 2280 matches in the English Premier League and La Liga, represented at four nested spatial resolutions spanning a 64-fold range. Robustness is quantified from the strongly connected giant component (SCGC) under random and topology-based targeted edge removal using a susceptibility-defined finite-network pseudo-critical threshold. At the primary 6 × 4 (L2) resolution, 95.1% of matches are more robust to random than targeted removal. The directed Molloy–Reed (MR) prediction changes from complete inapplicability at the finest scale to approximate unbiasedness at L2, showing that mean-field validity is representation dependent. Partial correlations and multivariate regression show that the apparent effect of mean degree is largely absorbed by the directed degree-distribution parameter, whereas flow hierarchy retains the largest independent contribution. A qualitative comparison with classical synthetic networks places the Barabási–Albert model closest to the empirical networks in the joint profile of random-failure and targeted-attack thresholds, without implying a preferential-attachment mechanism. Finally, edge sensitivity decomposes team-level SCGC robustness to individual players. These findings establish soccer passing networks as a finite, multiscale test bed for directed percolation theory and provide a topology-based framework for identifying structurally critical passing relations.
{"title":"Scale-dependent applicability of directed mean-field percolation in soccer passing networks","authors":"Kongyun Huang, Changjing Zhou, Xiuyuan Xiong, Xudong Yang, Yingzhe Song, Kai Xu, Johann H. Martínez, Miguel-Ángel Gómez-Ruano, Javier M. Buldú","doi":"10.1016/j.chaos.2026.119356","DOIUrl":"https://doi.org/10.1016/j.chaos.2026.119356","url":null,"abstract":"Mean-field percolation theory offers analytical predictions for network robustness, but its empirical validity for finite, directed, spatial networks depends on how those networks are represented. We analyse directed bond percolation in 4560 team-match pitch-player passing networks from 2280 matches in the English Premier League and La Liga, represented at four nested spatial resolutions spanning a 64-fold range. Robustness is quantified from the strongly connected giant component (SCGC) under random and topology-based targeted edge removal using a susceptibility-defined finite-network pseudo-critical threshold. At the primary 6 × 4 (L2) resolution, 95.1% of matches are more robust to random than targeted removal. The directed Molloy–Reed (MR) prediction changes from complete inapplicability at the finest scale to approximate unbiasedness at L2, showing that mean-field validity is representation dependent. Partial correlations and multivariate regression show that the apparent effect of mean degree is largely absorbed by the directed degree-distribution parameter, whereas flow hierarchy retains the largest independent contribution. A qualitative comparison with classical synthetic networks places the Barabási–Albert model closest to the empirical networks in the joint profile of random-failure and targeted-attack thresholds, without implying a preferential-attachment mechanism. Finally, edge sensitivity decomposes team-level SCGC robustness to individual players. These findings establish soccer passing networks as a finite, multiscale test bed for directed percolation theory and provide a topology-based framework for identifying structurally critical passing relations.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"11 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149274897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-27DOI: 10.1016/j.chaos.2026.119389
Yutong Li, Zhehua Zhou, Dong Xue, Stefano Boccaletti, Fangzhou Liu
The percolation, as an important theoretical tool for studying the robustness of networks, is continuously improved and explored on both ordinary graphs and hypergraphs. Given that most existing studies treat percolation as a single random event and overlook the fact that the collapse of real-world networks is a targeted and gradual process, we propose a node-targeted multi-step percolation model. In this model, the network undergoes multiple rounds of percolation processes, with the input for each percolation being the residual network after the previous percolation ends. Additionally, during each round of percolation, the failure probability of each node is related to the structure of the current residual network. It is worth noting that we have proposed a theoretical framework based on generating functions to predict the changes in the giant connected components of the networks during the multi-step percolation process, which has satisfactory predictive performance when the network satisfy the assumptions of being approximately locally treelike and having a degree distribution without extreme heavy-tailed characteristics. Furthermore, through tests on randomly generated ordinary graphs and hypergraphs, we find that networks with Poisson degree/hyperdegree distributions are often more vulnerable than those with power-law degree/hyperdegree distributions when facing the proposed node-targeted multi-step percolation process.
{"title":"Node-targeted multi-step percolation on networks","authors":"Yutong Li, Zhehua Zhou, Dong Xue, Stefano Boccaletti, Fangzhou Liu","doi":"10.1016/j.chaos.2026.119389","DOIUrl":"https://doi.org/10.1016/j.chaos.2026.119389","url":null,"abstract":"The percolation, as an important theoretical tool for studying the robustness of networks, is continuously improved and explored on both ordinary graphs and hypergraphs. Given that most existing studies treat percolation as a single random event and overlook the fact that the collapse of real-world networks is a targeted and gradual process, we propose a node-targeted multi-step percolation model. In this model, the network undergoes multiple rounds of percolation processes, with the input for each percolation being the residual network after the previous percolation ends. Additionally, during each round of percolation, the failure probability of each node is related to the structure of the current residual network. It is worth noting that we have proposed a theoretical framework based on generating functions to predict the changes in the giant connected components of the networks during the multi-step percolation process, which has satisfactory predictive performance when the network satisfy the assumptions of being approximately locally treelike and having a degree distribution without extreme heavy-tailed characteristics. Furthermore, through tests on randomly generated ordinary graphs and hypergraphs, we find that networks with Poisson degree/hyperdegree distributions are often more vulnerable than those with power-law degree/hyperdegree distributions when facing the proposed node-targeted multi-step percolation process.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"34 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149274890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-27DOI: 10.1016/j.chaos.2026.119417
Bing-ling Cen, Kai-yu Tian, Hua Kuang, Yu Xue, Ke-zhao Bai
Vehicle-to-everything (V2X) communication technology has been widely recognized as a transformation technology for optimizing traffic flow and improving road traffic safety. In this paper, considering that connected and automated vehicles (CAVs) can capture the state information of multiple preceding vehicles via V2X information interaction, we incorporate communication effects into an extended car-following model and derive its corresponding macroscopic continuum formulation. The linear stability condition is derived for uniform initial flow under small perturbations. By tuning key system parameters, the existence conditions and types of Hopf bifurcation are rigorously obtained. Finally, numerical simulations are conducted using the MatCont toolbox to determine the positions and types of Hopf bifurcations for comparative verification.
{"title":"Hopf bifurcation analysis for a continuum traffic flow model considering communication effect under V2X environment","authors":"Bing-ling Cen, Kai-yu Tian, Hua Kuang, Yu Xue, Ke-zhao Bai","doi":"10.1016/j.chaos.2026.119417","DOIUrl":"https://doi.org/10.1016/j.chaos.2026.119417","url":null,"abstract":"Vehicle-to-everything (V2X) communication technology has been widely recognized as a transformation technology for optimizing traffic flow and improving road traffic safety. In this paper, considering that connected and automated vehicles (CAVs) can capture the state information of multiple preceding vehicles via V2X information interaction, we incorporate communication effects into an extended car-following model and derive its corresponding macroscopic continuum formulation. The linear stability condition is derived for uniform initial flow under small perturbations. By tuning key system parameters, the existence conditions and types of Hopf bifurcation are rigorously obtained. Finally, numerical simulations are conducted using the MatCont toolbox to determine the positions and types of Hopf bifurcations for comparative verification.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"26 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149274889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-26DOI: 10.1016/j.chaos.2026.119385
Xiwei Liu, Zeshen Tang, Xinzhi Liu, Yu Zhang
This paper investigates quasi-containment control (Q-ContCtrl) for multiweighted and directed complex networks. Containment control for multiweighted and directed networks is more challenging than in previous works due to the presence of an intrinsic nonlinear function and multiple weights, where containment control means an affine combination but not merely the convex combination of states. By virtue of a new assumption on the intrinsic function of complex networks, we prove that Q-ContCtrl may emerge, i.e., the error remains bounded but does not converge to zero. Moreover, multiple outer and inner coupling matrices are shown to have a significant impact on the proposed Q-ContCtrl. Furthermore, we apply the prescribed-time technique to the coupling strength and achieve containment control at the prescribed time. Finally, we consider matrix-weighted networks as an application, for which synchronization and Q-ContCtrl are derived. Numerical simulations verify the theoretical results.
{"title":"Quasi-containment control for multiweighted networks","authors":"Xiwei Liu, Zeshen Tang, Xinzhi Liu, Yu Zhang","doi":"10.1016/j.chaos.2026.119385","DOIUrl":"https://doi.org/10.1016/j.chaos.2026.119385","url":null,"abstract":"This paper investigates quasi-containment control (Q-ContCtrl) for multiweighted and directed complex networks. Containment control for multiweighted and directed networks is more challenging than in previous works due to the presence of an intrinsic nonlinear function and multiple weights, where containment control means an affine combination but not merely the convex combination of states. By virtue of a new assumption on the intrinsic function of complex networks, we prove that Q-ContCtrl may emerge, i.e., the error remains bounded but does not converge to zero. Moreover, multiple outer and inner coupling matrices are shown to have a significant impact on the proposed Q-ContCtrl. Furthermore, we apply the prescribed-time technique to the coupling strength and achieve containment control at the prescribed time. Finally, we consider matrix-weighted networks as an application, for which synchronization and Q-ContCtrl are derived. Numerical simulations verify the theoretical results.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"64 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149274896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-26DOI: 10.1016/j.chaos.2026.119367
Karla González, Ariel Sandoval, Denisse Pastén
The displacement between the Nazca and South American plates has produced three large earthquakes in the last 16 years in Chile. In this work, we analyze these three large earthquakes through fractal dimension, spatial and temporal, and the b value obtained from the Gutenberg–Richter law. We found an unexpected relationship between the time evolution of these two fractal dimensions and the well-known b value. This analysis provides a relevant perspective on the temporal and spatial complexity of seismic activity and its patterns. Also, this methodological framework demonstrated robustness in identifying phases of energy accumulation and release in subduction zones.
{"title":"Evolution of the temporal and spatial fractal dimension for three large earthquakes in Chile","authors":"Karla González, Ariel Sandoval, Denisse Pastén","doi":"10.1016/j.chaos.2026.119367","DOIUrl":"https://doi.org/10.1016/j.chaos.2026.119367","url":null,"abstract":"The displacement between the Nazca and South American plates has produced three large earthquakes in the last 16 years in Chile. In this work, we analyze these three large earthquakes through fractal dimension, spatial and temporal, and the <mml:math altimg=\"si26.svg\" display=\"inline\"><mml:mi>b</mml:mi></mml:math> value obtained from the Gutenberg–Richter law. We found an unexpected relationship between the time evolution of these two fractal dimensions and the well-known <mml:math altimg=\"si26.svg\" display=\"inline\"><mml:mi>b</mml:mi></mml:math> value. This analysis provides a relevant perspective on the temporal and spatial complexity of seismic activity and its patterns. Also, this methodological framework demonstrated robustness in identifying phases of energy accumulation and release in subduction zones.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"13 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149274962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-25DOI: 10.1016/j.chaos.2026.119373
Barbara Wolnik, Dominik Michał Falkiewicz, Witold Bołt, Adam Rutkowski, Bernard De Baets
This paper presents a novel approach to the description and understanding of two-dimensional binary cellular automata with the Moore neighborhood that preserve the number of active cells. Such dynamical systems are known to successfully capture particle dynamics and are often used as theoretical models of physical processes where some conservation laws have to be taken into account. Unfortunately, to date, there are no tools for designing such non-trivial cellular utomata or for studying their properties, not to mention finding them all and describing their dynamics (even the order of magnitude of their number is unknown). We believe that the novel framework unfolded in this paper will make it possible to overcome all these challenges.
{"title":"Conditional traffic-like rules for particle-flow simulation in cellular automata","authors":"Barbara Wolnik, Dominik Michał Falkiewicz, Witold Bołt, Adam Rutkowski, Bernard De Baets","doi":"10.1016/j.chaos.2026.119373","DOIUrl":"https://doi.org/10.1016/j.chaos.2026.119373","url":null,"abstract":"This paper presents a novel approach to the description and understanding of two-dimensional binary cellular automata with the Moore neighborhood that preserve the number of active cells. Such dynamical systems are known to successfully capture particle dynamics and are often used as theoretical models of physical processes where some conservation laws have to be taken into account. Unfortunately, to date, there are no tools for designing such non-trivial cellular utomata or for studying their properties, not to mention finding them all and describing their dynamics (even the order of magnitude of their number is unknown). We believe that the novel framework unfolded in this paper will make it possible to overcome all these challenges.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"12 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149274899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：