Heteroclinic cycles and chaos in a class of 3D three-zone piecewise affine systems

被引：16
|
作者：
Lu, Kai [1 ]
Yang, Qigui [1 ]
Xu, Wenjing [2 ]
机构：
[1] South China Univ Technol, Dept Math, Guangzhou 510640, Guangdong, Peoples R China
[2] Northwestern Polytech Univ, Sch Sci, Xian 710129, Shaanxi, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 478卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Chaos; Heteroclinic cycle; Poincare map; Piecewise affine system; Discontinuous boundary; HOMOCLINIC ORBITS; SHILNIKOV CHAOS; CONNECTIONS; SADDLE;
D O I：
10.1016/j.jmaa.2019.04.070
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Little seems to be known about heteroclinic cycles and chaos in three-dimensional piecewise smooth dynamical systems with two or more discontinuous boundaries. This article presents a new class of three-dimensional three-zone piecewise affine systems with two discontinuous boundaries and provides some criteria for the existence of heteroclinic cycles in the following cases: (i) one saddle point and two focus points, (ii) two saddle points and one focus point, and (iii) three saddle points. Moreover, sufficient conditions for the existence of chaos are established. Finally, two numerical examples are provided to show the feasibility of our theoretical approach. (C) 2019 Elsevier Inc. All rights reserved.
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页码：58 / 81
页数：24
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