IF 2.7 2区数学

Chaos Pub Date : 2025-01-01 DOI: 10.1063/5.0251071

M Hillebrand, B Many Manda, G Kalosakas, E Gerlach, Ch Skokos

引用次数: 0

Proportions of incommensurate, resonant, and chaotic orbits for torus maps. 环面地图中不相称、共振和混沌轨道的比例。

IF 2.7 2区数学

Chaos Pub Date : 2025-01-01 DOI: 10.1063/5.0226617

E Sander, J D Meiss

引用次数: 0

Synchronization in spiking neural networks with short and long connections and time delays.

IF 2.7 2区数学

Chaos Pub Date : 2025-01-01 DOI: 10.1063/5.0158186

Lionel Kusch, Martin Breyton, Damien Depannemaecker, Spase Petkoski, Viktor K Jirsa

{"title":"Synchronization in spiking neural networks with short and long connections and time delays.","authors":"Lionel Kusch, Martin Breyton, Damien Depannemaecker, Spase Petkoski, Viktor K Jirsa","doi":"10.1063/5.0158186","DOIUrl":"https://doi.org/10.1063/5.0158186","url":null,"abstract":"Synchronization is fundamental for information processing in oscillatory brain networks and is strongly affected by time delays via signal propagation along long fibers. Their effect, however, is less evident in spiking neural networks given the discrete nature of spikes. To bridge the gap between these different modeling approaches, we study the synchronization conditions, dynamics underlying synchronization, and the role of the delay of a two-dimensional network model composed of adaptive exponential integrate-and-fire neurons. Through parameter exploration of neuronal and network properties, we map the synchronization behavior as a function of unidirectional long-range connection and the microscopic network properties and demonstrate that the principal network behaviors comprise standing or traveling waves of activity and depend on noise strength, E/I balance, and voltage adaptation, which are modulated by the delay of the long-range connection. Our results show the interplay of micro- (single neuron properties), meso- (connectivity and composition of the neuronal network), and macroscopic (long-range connectivity) parameters for the emergent spatiotemporal activity of the brain.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143063956","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

Impact of human intervention and predator-prey dynamics on ecosystem virus transmission. 人类干预和捕食者-猎物动态对生态系统病毒传播的影响。

IF 2.7 2区数学

Chaos Pub Date : 2025-01-01 DOI: 10.1063/5.0247884

Shidong Zhai, Jiyu Zhang, Yuhan Tang, Jun Ma

{"title":"Impact of human intervention and predator-prey dynamics on ecosystem virus transmission.","authors":"Shidong Zhai, Jiyu Zhang, Yuhan Tang, Jun Ma","doi":"10.1063/5.0247884","DOIUrl":"https://doi.org/10.1063/5.0247884","url":null,"abstract":"Humans and predators occupy dominant positions in ecosystems and are generally believed to play a decisive role in maintaining ecosystem stability, particularly in the context of virus transmission. However, this may not always be the case. By establishing some ecosystem virus transmission models that cover both human perspectives and predators, we have drawn the following conclusions: (1) Controlling vaccination activities from the human perspective can potentially lower the transmission rate and improve herd immunity, thereby indirectly protecting unvaccinated risk groups. (2) In the ecosystem, the human perspective does not always determine the spread of viruses. Once the ecological balance between predators and prey is disrupted, there may be scenarios where predator populations die out, prey populations overpopulate, or both predators and prey go extinct. In such cases, the spread of the virus has little impact, and the system cannot restore itself to a new equilibrium state. In this case, even if humans intervene, it is difficult to change the fate of species extinction. (3) In situations where predator and prey populations maintain a stable state, human attitudes and actions are particularly critical. Human intervention can directly affect the transmission rate of the virus and the recovery rate of hosts, thereby rapidly reducing the infection rate and mitigating the harm caused by the virus. If humans do not intervene, predators may remain infected for a long time, thereby posing a serious threat to the ecosystem.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143001013","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

Synchronization stability of epileptic brain network with higher-order interactions. 具有高阶相互作用的癫痫脑网络的同步稳定性。

IF 2.7 2区数学

Chaos Pub Date : 2025-01-01 DOI: 10.1063/5.0226291

Zhaohui Li, Chenlong Wang, Mindi Li, Biyun Han, Xi Zhang, Xiaoxia Zhou

{"title":"Synchronization stability of epileptic brain network with higher-order interactions.","authors":"Zhaohui Li, Chenlong Wang, Mindi Li, Biyun Han, Xi Zhang, Xiaoxia Zhou","doi":"10.1063/5.0226291","DOIUrl":"https://doi.org/10.1063/5.0226291","url":null,"abstract":"Generally, epilepsy is considered as abnormally enhanced neuronal excitability and synchronization. So far, previous studies on the synchronization of epileptic brain networks mainly focused on the synchronization strength, but the synchronization stability has not yet been explored as deserved. In this paper, we propose a novel idea to construct a hypergraph brain network (HGBN) based on phase synchronization. Furthermore, we apply the synchronization stability framework of the nonlinear coupled oscillation dynamic model (generalized Kuramoto model) to investigate the HGBNs of epilepsy patients. Specifically, the synchronization stability of the epileptic brain is quantified by calculating the eigenvalue spectrum of the higher-order Laplacian matrix in HGBN. Results show that synchronization stability decreased slightly in the early stages of seizure but increased significantly prior to seizure termination. This indicates that an emergency self-regulation mechanism of the brain may facilitate the termination of seizures. Moreover, the variation in synchronization stability during epileptic seizures may be induced by the topological changes of epileptogenic zones (EZs) in HGBN. Finally, we verify that the higher-order interactions improve the synchronization stability of HGBN. This study proves the validity of the synchronization stability framework with the nonlinear coupled oscillation dynamical model in HGBN, emphasizing the importance of higher-order interactions and the influence of EZs on the termination of epileptic seizures.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143001084","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

Mean-field approximation for networks with synchrony-driven adaptive coupling.

IF 2.7 2区数学

Chaos Pub Date : 2025-01-01 DOI: 10.1063/5.0231457

N Fennelly, A Neff, R Lambiotte, A Keane, Á Byrne

{"title":"Mean-field approximation for networks with synchrony-driven adaptive coupling.","authors":"N Fennelly, A Neff, R Lambiotte, A Keane, Á Byrne","doi":"10.1063/5.0231457","DOIUrl":"https://doi.org/10.1063/5.0231457","url":null,"abstract":"Synaptic plasticity plays a fundamental role in neuronal dynamics, governing how connections between neurons evolve in response to experience. In this study, we extend a network model of θ-neuron oscillators to include a realistic form of adaptive plasticity. In place of the less tractable spike-timing-dependent plasticity, we employ recently validated phase-difference-dependent plasticity rules, which adjust coupling strengths based on the relative phases of θ-neuron oscillators. We explore two distinct implementations of this plasticity: pairwise updates to individual coupling strengths and global updates applied to the mean coupling strength. We derive a mean-field approximation and assess its accuracy by comparing it to θ-neuron simulations across various stability regimes. The synchrony of the system is quantified using the Kuramoto order parameter. Through bifurcation analysis and the calculation of maximal Lyapunov exponents, we uncover interesting phenomena such as bistability and chaotic dynamics via period-doubling and boundary crisis bifurcations. These behaviors emerge as a direct result of adaptive coupling and are absent in systems without such plasticity.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143051662","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

Selection and optimization of drive nodes in drive-response networks.

IF 2.7 2区数学

Chaos Pub Date : 2025-01-01 DOI: 10.1063/5.0226760

Zihao Yan, Ziye Fan, Jie Hu, Hui Liu, Xiaoqun Wu

{"title":"Selection and optimization of drive nodes in drive-response networks.","authors":"Zihao Yan, Ziye Fan, Jie Hu, Hui Liu, Xiaoqun Wu","doi":"10.1063/5.0226760","DOIUrl":"https://doi.org/10.1063/5.0226760","url":null,"abstract":"This paper considers the selection and optimization of drive nodes based on the controllability of multilayer networks. The intra-layer network topologies are arbitrary, and the node dynamics are linear time-invariant dynamical systems. The study focuses on the number and selection of drive nodes in a special class of drive-response networks. Several conclusions are drawn through the investigation: (1) All the drive nodes cannot be placed in the response layer but can be contained in the drive layer; (2) The minimum number of drive nodes placed in the drive layer is equal to the maximum geometric multiplicity of the system matrix of the drive layer; (3) The configuration of interlayer coupling weight significantly affects the number and distribution of drive nodes. Moreover, an optimization scheme is proposed based on the Gershgorin circle theorem, which aims to minimize the number of drive nodes in the entire network. This scheme ensures that regardless of the drive nodes originally needed, they can be reduced to the maximum geometric multiplicity of the system matrix of the drive layer. Numerical simulations on a general two-layer network as well as various synthetic networks are provided to validate the results.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143063911","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

A class of n-D Hamiltonian conservative chaotic systems with three-terminal memristor: Modeling, dynamical analysis, and FPGA implementation. 一类带有三端忆阻器的n-D哈密顿保守混沌系统：建模、动态分析和FPGA实现。

IF 2.7 2区数学

Chaos Pub Date : 2025-01-01 DOI: 10.1063/5.0238893

Ye Yuan, Fei Yu, Bohong Tan, Yuanyuan Huang, Wei Yao, Shuo Cai, Hairong Lin

{"title":"A class of n-D Hamiltonian conservative chaotic systems with three-terminal memristor: Modeling, dynamical analysis, and FPGA implementation.","authors":"Ye Yuan, Fei Yu, Bohong Tan, Yuanyuan Huang, Wei Yao, Shuo Cai, Hairong Lin","doi":"10.1063/5.0238893","DOIUrl":"https://doi.org/10.1063/5.0238893","url":null,"abstract":"Memristors are commonly used to introduce various chaotic systems and can be used to enhance their chaotic characteristics. However, due to the strict construction conditions of Hamiltonian systems, there has been limited research on the development of memristive Hamiltonian conservative chaotic systems (MHCCSs). In this work, a method for constructing three-terminal memristors is proposed, and the three-terminal memristors are incorporated into the Hamiltonian system, resulting in the development of a class of n-D MHCCS. Based on this method, we model a 4D MHCCS as a standard model for detailed dynamic analysis. The dynamic analysis reveals that the MHCCS exhibits complex dynamic behaviors, including conservativeness, symmetry, chaos depending on parameters, extreme multistability, and chaos under a wide parameter range. The dynamic analysis shows that MHCCS not only retains the favorable characteristics of a conservative system but also has more complex nonlinear dynamics due to the incorporation of memristors, thereby further enhancing its chaotic characteristics. Furthermore, the pseudo-random number generator based on the MHCCS has excellent randomness in terms of the NIST test. Finally, the physical realizability of the system is verified through Field Programmable Gate Array experiments. This study demonstrates that the constructed class of MHCCSs is a good entropy source that can be applied to various chaotic embedded systems, including secure communication, cryptographic system, and pseudo-random number generator.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142945607","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

Soliton and rogue wave excitations in the Chen-Lee-Liu derivative nonlinear Schrödinger equation with two complex PT-symmetric potentials. 具有两个复pt对称势的Chen-Lee-Liu导数非线性Schrödinger方程中的孤子和异常波激励。

IF 2.7 2区数学

Chaos Pub Date : 2025-01-01 DOI: 10.1063/5.0239750

Ping Liu, Yong Chen, Xuedong Chai

{"title":"Soliton and rogue wave excitations in the Chen-Lee-Liu derivative nonlinear Schrödinger equation with two complex PT-symmetric potentials.","authors":"Ping Liu, Yong Chen, Xuedong Chai","doi":"10.1063/5.0239750","DOIUrl":"https://doi.org/10.1063/5.0239750","url":null,"abstract":"We demonstrate that fundamental nonlinear localized modes can exist in the Chen-Lee-Liu equation modified by several parity-time (PT) symmetric complex potentials. The explicit formula of analytical solitons is derived from the physically interesting Scarf-II potential, and families of spatial solitons in internal modes are numerically captured under the optical lattice potential. By the spectral analysis of linear stability, we observe that these bright solitons can remain stable across a broad scope of potential parameters, despite the breaking of the corresponding linear PT-symmetric phases. When these bright spatial solitons interact with external incident waves, they can always maintain their original shape, while the external incident wave may remain unchanged or may generate a reflected wave after the interaction. Then, the adiabatic switching of potential parameters is carried out in a way that allows these bright solitons to be excited from one unstable bound state to another alternative stable bound state. Many other intriguing properties associated with these nonlinear localized modes including the lateral power flow are further analyzed meticulously. Various high-order rogue waves induced by modulation instability in these PT-symmetric systems are generated too. These results may be useful to construct novel optical soliton communication schemes or design related optical materials.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142945632","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

Survival properties and spread rates in non-autonomous spread models. 非自主扩散模型中的生存特性和扩散率。

IF 2.7 2区数学

Chaos Pub Date : 2025-01-01 DOI: 10.1063/5.0219391

Jung-Chao Ban, Jyy-I Hong, Cheng-Yu Tsai, Chu-Yang Tsou

引用次数: 0

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