一类新混沌系统的几何分析

Abstract

Abstract:

Based on Poincaré compactification technology, the global dynamics behavior of three dimensional chaotic system is studied. The results show that the equilibria at infinity are unstable and highly degraded. The controlled system with a linear controller which does not change the singularity structure has a bunch of degenerate singular orbits. The chaotic attractors for the system in the case of small parameters b and c are found numerically, and thus the nearby singularly degenerate heteroclinic cycles. It is hoped that the investigation of this paper will be quite beneficial for further studies of the geometrical structure for the chaotic attractor.

Key words: Poincaré compactification, Singular point at infinity, Singularly degenerate heteroclinic cycles, Chaotic system

CLC Number:

O175

Xiezhen Huang,Yongjian Liu,Qiujian Huang. Geometric Analysis of a Class of the New Chaotic System[J].Acta mathematica scientia,Series A, 2019, 39(2): 339-347.

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Figures/Tables 6

References 27

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条件		O(0, 0)的类型
a_2m≠0	b_n=0	退化的奇点

条件			O(0, 0)的类型
a_2m+1 < 0	b_n≠0	n=m, λ≥0且n是偶数 n < m且n是偶数	结点

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Geometric Analysis of a Class of the New Chaotic System

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