Chaos Generated by a Class of 3D Three-Zone Piecewise Affine Systems with Coexisting Singular Cycles

被引：11
|
作者：
Lu, Kai [1 ]
Xu, Wenjing [2 ]
Yang, Qigui [3 ]
机构：
[1] Chongqing Univ Posts & Telecommun, Sch Sci, Chongqing 400065, Peoples R China
[2] Northwestern Polytech Univ, Sch Sci, Xian 710129, Peoples R China
[3] South China Univ Technol, Sch Math, Guangzhou 510000, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2020年 / 30卷 / 14期
基金：
中国国家自然科学基金;
关键词：
Chaos; coexistence of homoclinic cycles; coexistence of heteroclinic cycles; bifurcation; dynamical behavior; piecewise affine system; HETEROCLINIC CYCLES; HOMOCLINIC ORBITS; EXISTENCE; LORENZ; CONNECTIONS; DYNAMICS; SADDLE; POINT;
D O I：
10.1142/S0218127420502090
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is a significant and challenging task to detect both the coexistence of singular cycles, mainly homoclinic and heteroclinic cycles, and chaos induced by the coexistence in nonsmooth systems. By analyzing the dynamical behaviors on manifolds, this paper proposes some criteria to accurately locate the coexistence of homoclinic cycles and of heteroclinic cycles in a class of three-dimensional (3D) piecewise affine systems (PASs), respectively. It further establishes the existence conditions of chaos arising from such coexistence, and presents a mathematical proof by analyzing the constructed Poincare map. Finally, the simulations for two numerical examples are provided to validate the established results.
引用
收藏
页数：17
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