New geometric viewpoints to Chen chaotic system

Miskolc Mathematical Notes

article

Xiaoting Lu¹  Yongjian Liu²  Aimin Liu²  Chunsheng Feng³ 

[1] Guangxi Normal University, School of Mathematics and Statistics;Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University;School of Mathematics and Computational Science, Xiangtan University

关键词: Chen system;    homoclinic orbit;    torsion tensor;    tangent bundle;    chaos;   

DOI  :  10.18514/MMN.2022.3787

学科分类：数学（综合）

来源: Miskolci Egyetem

【 摘 要 】

This paper presents new geometric viewpoints to Chen chaotic system. Firstly, the existence of two nontransverse homoclinic orbits in Chen system is rigorously proved beyond the classical parameters. Secondly, combined with the theory of tangent bundle, a new geometric viewpoint is given to explore chaos mechanism of Chen system.The fundamental geometric definition of tangent bundle and the essential role of nonlinear connection between the tangent space and the base space are described. By introducing the geometrical viewpoints of second order system governed by Lie-Poisson equation, some geometric invariants of Chen system can be obtained. Furthermore, the torsion tensor as one of the geometric invariants is obtained, and it gives the geometrical interpretation to the chaotic behavior of Chen system. Finally, the torsion tensor of Chen system and Lorenz system are also compared. The obtaining results show that torsion tensor change will lead the Chen system from periodic to chaotic, which is not found in Lorenz system.

【 授权许可】

CC BY