Li-Yorke chaos of linear differential equations in a finite-dimensional space with a weak topology

Xu Zhang; Nan Jiang; Qigui Yang; Guanrong Chen

doi:10.1063/5.0163463

Li-Yorke chaos of linear differential equations in a finite-dimensional space with a weak topology

Chaos. 2023 Aug 1;33(8):081104. doi: 10.1063/5.0163463.

Authors

Xu Zhang¹, Nan Jiang¹, Qigui Yang², Guanrong Chen³

Affiliations

¹ Department of Mathematics, Shandong University, Weihai, Shandong 264209, China.
² School of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640, China.
³ Department of Electrical Engineering, City University of Hong Kong, Hong Kong SAR, China.

PMID: 38060786
DOI: 10.1063/5.0163463

Abstract

Li-Yorke chaos of linear differential equations in a finite-dimensional space with a weak topology is introduced. Based on this topology on the Euclidean space, a flow generated from a linear differential equation is proved to be Li-Yorke chaotic under certain conditions, which is in sharp contract to the well-known fact that linear differential equations cannot be chaotic in a finite-dimensional space with a strong topology.