具有扩散的耦合蔡氏电路中的奇异摄动分析。

Singular perturbation analysis in a coupled Chua's circuit with diffusion.

作者信息

Li Zhengkang, Liu Xingbo

机构信息

School of Mathematics, China University of Mining and Technology, Xuzhou 221116, People's Republic of China.

School of Mathematical Sciences, Key Laboratory of MEA (Ministry of Education) and Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, People's Republic of China.

出版信息

Chaos. 2023 Oct 1;33(10). doi: 10.1063/5.0152679.

DOI:10.1063/5.0152679

PMID:37831794

Abstract

This paper is concerned with the traveling wave solutions of a singularly perturbed system, which arises from the coupled arrays of Chua's circuit. By the geometric singular perturbation theory and invariant manifold theory, we prove that there exists a heteroclinic cycle consisting of the traveling front and back waves with the same wave speed. In particular, the expression of corresponding wave speed is also obtained. Furthermore, we show that the chaotic behavior induced by this heteroclinic cycle is hyperchaos.

摘要

本文关注一个奇异摄动系统的行波解，该系统源自蔡氏电路的耦合阵列。通过几何奇异摄动理论和不变流形理论，我们证明存在一个由具有相同波速的前行波和后行波组成的异宿环。特别地，还得到了相应波速的表达式。此外，我们表明由这个异宿环诱导的混沌行为是超混沌。