Persistent Synchronization of Heterogeneous Networks with Time-Dependent Linear Diffusive Coupling

IF 1.7 4区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Applied Dynamical Systems Pub Date : 2024-06-19 DOI:10.1137/23m1602024

Hildeberto Jardón-Kojakhmetov, Christian Kuehn, Iacopo P. Longo

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引用次数: 0

Abstract

SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 2, Page 1540-1578, June 2024.
Abstract.We study synchronization for linearly coupled temporal networks of heterogeneous time-dependent nonlinear agents via the convergence of attracting trajectories of each node. The results are obtained by constructing and studying the stability of a suitable linear nonautonomous problem bounding the evolution of the synchronization errors. Both the case of the entire network and that of only a cluster are addressed, and the persistence of the obtained synchronization against perturbation is also discussed. Furthermore, a sufficient condition for the existence of attracting trajectories of each node is given. In all cases, the considered dependence on time requires only local integrability, which is a very mild regularity assumption. Moreover, our results mainly depend on the network structure and its properties and achieve synchronization up to a constant in finite time. Hence they are quite suitable for applications. The applicability of the results is showcased via several examples: coupled van der Pol/FitzHugh–Nagumo oscillators, weighted/signed opinion dynamics, and coupled Lorenz systems.

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具有时变线性扩散耦合的异构网络的持久同步性

SIAM 应用动力系统期刊》第 23 卷第 2 期第 1540-1578 页，2024 年 6 月。摘要.我们通过每个节点的吸引轨迹的收敛，研究了由异构时间依赖非线性代理组成的线性耦合时间网络的同步问题。结果是通过构建和研究约束同步误差演化的合适线性非自治问题的稳定性得到的。研究既涉及整个网络的情况，也涉及仅有一个集群的情况，还讨论了所获得的同步对扰动的持久性。此外，还给出了每个节点存在吸引轨迹的充分条件。在所有情况下，所考虑的时间依赖性只要求局部可整性，这是一个非常温和的正则性假设。此外，我们的结果主要取决于网络结构及其特性，并能在有限时间内实现同步至常数。因此，它们非常适合应用。我们通过几个例子展示了这些结果的适用性：耦合范德波尔/菲茨休-纳古莫振荡器、加权/有符号舆论动力学和耦合洛伦兹系统。

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来源期刊

SIAM Journal on Applied Dynamical Systems 物理-物理：数学物理

CiteScore

3.60

自引率

4.80%

发文量

审稿时长

6 months

期刊介绍： SIAM Journal on Applied Dynamical Systems (SIADS) publishes research articles on the mathematical analysis and modeling of dynamical systems and its application to the physical, engineering, life, and social sciences. SIADS is published in electronic format only.