全局耦合地图中的横向 Lyapunov 指数和嵌合体

IF 1.7 4区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Applied Dynamical Systems Pub Date : 2024-07-19 DOI:10.1137/23m1603339

Théophile Caby, Pierre Guiraud

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引用次数: 0

摘要

SIAM 应用动力系统期刊》，第 23 卷第 3 期，第 1946-1965 页，2024 年 9 月。摘要：我们研究了全局耦合映射系统中嵌合体的稳定性和长期动力学。特别是，我们建立了包含同步单元的系统状态的横向 Lyapunov 指数公式。我们利用这个公式提出了具有混沌动力学和周期行为的吸引嵌合体的数值证据。我们还证明，至少对于多项式局部映射，吸引周期性循环倾向于属于簇空间，更一般地说，在强耦合状态下，嵌合体轨道的极限集的勒贝格度量为零。

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Transverse Lyapunov Exponent and Chimeras in Globally Coupled Maps

SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 3, Page 1946-1965, September 2024.
Abstract.We study the stability properties and the long-term dynamics of chimeras in systems of globally coupled maps. In particular, we establish a formula for the transverse Lyapunov exponent of the states of the system containing synchronized units. We use this formula to present numerical evidence of attracting chimeras having chaotic dynamics as well as periodic behaviors. We also show that, at least for polynomial local maps, attracting periodic cycles tend to belong to cluster spaces, and, more generally, limit sets of chimera orbits have zero Lebesgue measure for strong coupling regimes.

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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.