NEW GEOMETRIC VIEWPOINTS TO CHEN CHAOTIC SYSTEM

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 geo-metrical 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 geomet-ric invariants is obtained, and it gives the geometrical interpretation to the chaotic behaviour of Chen system. inally, the torsion tensor of Chen system and Lorenz system are also compared. The obtain-ing results show that torsion tensor change will lead the Chen system from periodic to chaotic, which is not found in Lorenz system.