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Pulses in singularly perturbed reaction-diffusion systems with slowly mixed nonlinearity. 具有缓慢混合非线性的奇异扰动反应-扩散系统中的脉冲。
IF 2.7 2区 数学
Chaos Pub Date : 2024-11-01 DOI: 10.1063/5.0228472
Yuanxian Chen, Yuhua Cai, Jianhe Shen
{"title":"Pulses in singularly perturbed reaction-diffusion systems with slowly mixed nonlinearity.","authors":"Yuanxian Chen, Yuhua Cai, Jianhe Shen","doi":"10.1063/5.0228472","DOIUrl":"https://doi.org/10.1063/5.0228472","url":null,"abstract":"<p><p>This article is concerned with the existence and spectral stability of pulses in singularly perturbed two-component reaction-diffusion systems with slowly mixed nonlinearity. In this paper, the slow nonlinearity is referred to be \"mixed\" in the sense that it is generated by a trigonometric function multiplied by a power function. We demonstrate via geometric singular perturbation theory that this model can support both the single-pulse and the double-hump solutions. The presence of the slowly mixed nonlinearity complicates the stability analysis on pulses, since the conditions that govern their stability can no longer be explicitly computed. We remove this difficulty by introducing the hypergeometric functions followed by a comparison theorem. By doing so, the \"slow-fast\" eigenvalues can be determined via the nonlocal eigenvalue problem method. We prove that the double-hump solution is always unstable, while the single-pulse solution can be stable under certain parameter conditions.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 11","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142557289","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
Vegetation restoration strategies in arid or semi-arid regions-From the perspective of optimal control. 干旱或半干旱地区的植被恢复战略--从优化控制的角度。
IF 2.7 2区 数学
Chaos Pub Date : 2024-11-01 DOI: 10.1063/5.0206880
Li-Feng Hou, Shu-Peng Gao, Li-Li Chang, Yong-Ping Wu, Guo-Lin Feng, Zhen Wang, Gui-Quan Sun
{"title":"Vegetation restoration strategies in arid or semi-arid regions-From the perspective of optimal control.","authors":"Li-Feng Hou, Shu-Peng Gao, Li-Li Chang, Yong-Ping Wu, Guo-Lin Feng, Zhen Wang, Gui-Quan Sun","doi":"10.1063/5.0206880","DOIUrl":"https://doi.org/10.1063/5.0206880","url":null,"abstract":"<p><p>Inappropriate human activities contribute to the degradation of ecosystems in arid or semi-arid regions. Therefore, emphasizing the importance of strategies for restoring vegetation in these areas cannot be overstated. However, there has been insufficient research on how to develop effective restoration strategies at minimal cost. This paper addresses this gap by studying how optimizing the spatiotemporal distribution of human activities through local and boundary controls can reduce the level of desertification in vegetation pattern structures, thereby facilitating the recovery of arid land vegetation. The results indicate that vegetation restoration depends on the proportion and number of human activity areas, with a trade-off between them. Furthermore, consistent conclusions were obtained on circular regions, demonstrating the robustness of the approach to boundary shapes. This paper aims to offer new insights into the restoration of arid land vegetation and the prevention of catastrophic ecosystem changes from the perspective of optimal control.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 11","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142575323","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
An investigation of escape and scaling properties of a billiard system. 台球系统的逃逸和缩放特性研究。
IF 2.7 2区 数学
Chaos Pub Date : 2024-11-01 DOI: 10.1063/5.0222215
Matheus Rolim Sales, Daniel Borin, Diogo Ricardo da Costa, José Danilo Szezech, Edson Denis Leonel
{"title":"An investigation of escape and scaling properties of a billiard system.","authors":"Matheus Rolim Sales, Daniel Borin, Diogo Ricardo da Costa, José Danilo Szezech, Edson Denis Leonel","doi":"10.1063/5.0222215","DOIUrl":"https://doi.org/10.1063/5.0222215","url":null,"abstract":"<p><p>We investigate some statistical properties of escaping particles in a billiard system whose boundary is described by two control parameters with a hole on its boundary. Initially, we analyze the survival probability for different hole positions and sizes. We notice that the survival probability follows an exponential decay with a characteristic power-law tail when the hole is positioned partially or entirely over large stability islands in phase space. We find that the survival probability exhibits scaling invariance with respect to the hole size. In contrast, the survival probability for holes placed in predominantly chaotic regions deviates from the exponential decay. We introduce two holes simultaneously and investigate the complexity of the escape basins for different hole sizes and control parameters by means of the basin entropy and the basin boundary entropy. We find a non-trivial relation between these entropies and the system's parameters and show that the basin entropy exhibits scaling invariance for a specific control parameter interval.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 11","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142603069","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
Symmetry breaker governs synchrony patterns in neuronal inspired networks. 对称性断路器制约着神经元启发网络的同步模式。
IF 2.7 2区 数学
Chaos Pub Date : 2024-11-01 DOI: 10.1063/5.0209865
Anil Kumar, Edmilson Roque Dos Santos, Paul J Laurienti, Erik Bollt
{"title":"Symmetry breaker governs synchrony patterns in neuronal inspired networks.","authors":"Anil Kumar, Edmilson Roque Dos Santos, Paul J Laurienti, Erik Bollt","doi":"10.1063/5.0209865","DOIUrl":"10.1063/5.0209865","url":null,"abstract":"<p><p>Experiments in the human brain reveal switching between different activity patterns and functional network organization over time. Recently, multilayer modeling has been employed across multiple neurobiological levels (from spiking networks to brain regions) to unveil novel insights into the emergence and time evolution of synchrony patterns. We consider two layers with the top layer directly coupled to the bottom layer. When isolated, the bottom layer would remain in a specific stable pattern. However, in the presence of the top layer, the network exhibits spatiotemporal switching. The top layer in combination with the inter-layer coupling acts as a symmetry breaker, governing the bottom layer and restricting the number of allowed symmetry-induced patterns. This structure allows us to demonstrate the existence and stability of pattern states on the bottom layer, but most remarkably, it enables a simple mechanism for switching between patterns based on the unique symmetry-breaking role of the governing layer. We demonstrate that the symmetry breaker prevents complete synchronization in the bottom layer, a situation that would not be desirable in a normal functioning brain. We illustrate our findings using two layers of Hindmarsh-Rose (HR) oscillators, employing the Master Stability function approach in small networks to investigate the switching between patterns.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 11","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142582402","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
Shrinking shrimp-shaped domains and multistability in the dissipative asymmetric kicked rotor map. 耗散非对称踢转子图中的收缩虾形域和多稳定性。
IF 2.7 2区 数学
Chaos Pub Date : 2024-11-01 DOI: 10.1063/5.0233324
Matheus Rolim Sales, Michele Mugnaine, Edson Denis Leonel, Iberê L Caldas, José D Szezech
{"title":"Shrinking shrimp-shaped domains and multistability in the dissipative asymmetric kicked rotor map.","authors":"Matheus Rolim Sales, Michele Mugnaine, Edson Denis Leonel, Iberê L Caldas, José D Szezech","doi":"10.1063/5.0233324","DOIUrl":"10.1063/5.0233324","url":null,"abstract":"<p><p>An interesting feature in dissipative nonlinear systems is the emergence of characteristic domains in parameter space that exhibit periodic temporal evolution, known as shrimp-shaped domains. We investigate the parameter space of the dissipative asymmetric kicked rotor map and show that, in the regime of strong dissipation, the shrimp-shaped domains repeat themselves as the nonlinearity parameter increases while maintaining the same period. We analyze the dependence of the length of each periodic domain with the nonlinearity parameter, revealing that it follows a power law with the same exponent regardless of the dissipation parameter. Additionally, we find that the distance between adjacent shrimp-shaped domains is scaling invariant with respect to the dissipation parameter. Furthermore, we show that for weaker dissipation, a multistable scenario emerges within the periodic domains. We find that as the dissipation gets weaker, the ratio of multistable parameters for each periodic domain increases, and the area of the periodic basin decreases as the nonlinearity parameter increases.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 11","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142638515","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
Chaotic dynamics in a class of generalized memristive maps. 一类广义记忆图中的混沌动力学。
IF 2.7 2区 数学
Chaos Pub Date : 2024-11-01 DOI: 10.1063/5.0237251
Iram Hussan, Manyu Zhao, Xu Zhang
{"title":"Chaotic dynamics in a class of generalized memristive maps.","authors":"Iram Hussan, Manyu Zhao, Xu Zhang","doi":"10.1063/5.0237251","DOIUrl":"https://doi.org/10.1063/5.0237251","url":null,"abstract":"<p><p>The memory effects of the memristors in nonlinear systems make the systems generate complicated dynamics, which inspires the development of the applications of memristors. In this article, the model of the discrete memristive systems with the generalized Ohm's law is introduced, where the classical Ohm's law is a linear relationship between voltage and current, and a generalized Ohm's law is a nonlinear relationship. To illustrate the rich dynamics of this model, the complicated dynamical behavior of three types of maps with three types of discrete memristances is investigated, where a cubic function representing a kind of generalized Ohm's law is used, and this cubic function is a simplified characteristic of the famous tunnel diode. The existence of attractors with one or two positive Lyapunov exponents (corresponding to chaotic or hyperchaotic dynamics) is obtained, and the coexistence of (infinitely) many attractors is observable. A hardware device is constructed to implement these maps and the analog voltage signals are experimentally acquired.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 11","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142616002","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
Model-free distributed state estimation with local measurements. 利用局部测量进行无模型分布式状态估计。
IF 2.7 2区 数学
Chaos Pub Date : 2024-11-01 DOI: 10.1063/5.0235313
Kepan Gao, Chenyu Ran, Xiaoling Wang, Liu Liu, Guo-Ping Jiang
{"title":"Model-free distributed state estimation with local measurements.","authors":"Kepan Gao, Chenyu Ran, Xiaoling Wang, Liu Liu, Guo-Ping Jiang","doi":"10.1063/5.0235313","DOIUrl":"10.1063/5.0235313","url":null,"abstract":"<p><p>In this paper, the state estimation problem of physical plants with unknown system dynamic is revisited from the perspective of limited output information measurement, which corresponds to those with characteristics of high-dimensional, wide-area coverage and scatter. Given this fact, a network of sensors are used to carry out the measurement with each one accessing only partial outputs of the targeted systems and a novel model-free state estimation approach, named distributed stochastic variational inference state estimation, is proposed. The key idea of this method is to compensate for the impacts of local output measurements by adding nearest-neighbor rule-based information interaction among estimators to complete the state estimation. It finds from the numerical experiments that the proposed method has clear advantages in both estimation accuracy and speed, and it also provides guidance on how to improve the efficiency of state estimation under local measurements.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 11","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142638513","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
Identifying influential nodes in social networks from the perspective of attack-defense game. 从攻防博弈的角度识别社交网络中具有影响力的节点。
IF 2.7 2区 数学
Chaos Pub Date : 2024-11-01 DOI: 10.1063/5.0240052
Wen Hu, Ye Deng, Yu Xiao, Jun Wu
{"title":"Identifying influential nodes in social networks from the perspective of attack-defense game.","authors":"Wen Hu, Ye Deng, Yu Xiao, Jun Wu","doi":"10.1063/5.0240052","DOIUrl":"https://doi.org/10.1063/5.0240052","url":null,"abstract":"<p><p>Influence spread analysis, a critical component of social network studies, focuses on the patterns and effects of information dissemination among interconnected entities. The core of influence spread analysis is to identify influential nodes that involve two distinct aspects: influence maximization (IM) and influence blocking maximization (IBM). However, when IM and IBM occur simultaneously, identifying influential nodes becomes an intricate decision-making challenge. This study addresses identifying influential nodes in social networks through an attack-defense game perspective, where an attacker maximizes influence and a defender minimizes it. We first develop a two-player static zero-sum game model considering resource constraints. Based on the equilibrium strategy of this game, we redefine the concept of influential nodes from various viewpoints. Extensive experiments on synthetic and real-world networks show that, in most cases, the defender preferentially defends critical nodes, while the attacker adopts the decentralized strategy. Only when resources are unevenly matched do both players tend to adopt centralized strategies. This study expands the connotation of influential nodes and provides a novel paradigm for the social network analysis with significant potential applications.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 11","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142557285","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
On the periodic behavior of the generalized Chazy differential equation. 论广义查兹微分方程的周期行为。
IF 2.7 2区 数学
Chaos Pub Date : 2024-11-01 DOI: 10.1063/5.0209050
Ziwei Zhuang, Changjian Liu, Jiahui Luo
{"title":"On the periodic behavior of the generalized Chazy differential equation.","authors":"Ziwei Zhuang, Changjian Liu, Jiahui Luo","doi":"10.1063/5.0209050","DOIUrl":"https://doi.org/10.1063/5.0209050","url":null,"abstract":"<p><p>We consider the periodic behavior of the generalized Chazy differential equation x⃛+|x|qx¨+k|x|qxx˙2=0, where q is a positive integer and k is a real number. We give a pure analysis on the existence of non-trivial periodic solutions for k=q+1 and the non-existence of them for k≠q+1. Our method is based on considering the projections of the orbits onto the phase plane (x,x˙). We find that a non-trivial periodic solution of the equation is equivalent to a closed curve formed by two equilibrium points and two orbits with some specific constraints in the corresponding planar system and that the existence of such closed curves can be obtained by the existence of real zeros of some returning map. Our conclusion covers all q, which completes a recent result.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 11","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142557288","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
Orbits of a system of three point vortices and the associated chaotic mixing. 三点旋涡系统的轨道及相关的混沌混合。
IF 2.7 2区 数学
Chaos Pub Date : 2024-11-01 DOI: 10.1063/5.0232416
David G Dritschel, Gregory N Dritschel, Richard K Scott
{"title":"Orbits of a system of three point vortices and the associated chaotic mixing.","authors":"David G Dritschel, Gregory N Dritschel, Richard K Scott","doi":"10.1063/5.0232416","DOIUrl":"https://doi.org/10.1063/5.0232416","url":null,"abstract":"<p><p>We study the general periodic motion of a set of three point vortices in the plane, as well as the potentially chaotic motion of one or more tracer particles. While the motion of three vortices is simple in that it can only be periodic, the actual orbits can be surprisingly complex and varied. This rich behavior arises from the existence of both co-linear and equilateral relative equilibria (steady motion in a rotating frame of reference). Here, we start from a general (unsteady) co-linear array with arbitrary vortex circulations. The subsequent motion may take the vortices close to a distinct co-linear relative equilibrium or to an equilateral one. Both equilibrium states are necessarily unstable, as we demonstrate by a linear stability analysis. We go on to study mixing by examining Poincaré sections and finite-time Lyapunov exponents. Both indicate widespread chaotic motion in general, implying that the motion of three vortices efficiently mixes the nearby surrounding fluid outside of small regions surrounding each vortex.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 11","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142603152","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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