Border collision bifurcations in 3D piecewise smooth chaotic circuit

doi:10.1007/s10483-016-2129-6

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (9): 1239-1250.doi: https://doi.org/10.1007/s10483-016-2129-6

Border collision bifurcations in 3D piecewise smooth chaotic circuit

Yinghui GAO¹, Xiangying MENG², Qishao LU³

1. School of Mathematics and System Sciences, LMIB of the Ministry of Education, Beihang University, Beijing 100191, China;
2. Department of Biology, University of Maryland, College Park, MD 20742, U. S. A.;
3. School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China

收稿日期:2015-12-25 修回日期:2016-03-11 出版日期:2016-09-01 发布日期:2016-09-01
通讯作者: Qishao LU E-mail:qishaolu@hotmail.com
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11272024, 11371046, and 11372017) and the Fundamental Research Funds for the Central Universities

Border collision bifurcations in 3D piecewise smooth chaotic circuit

Yinghui GAO¹, Xiangying MENG², Qishao LU³

1. School of Mathematics and System Sciences, LMIB of the Ministry of Education, Beihang University, Beijing 100191, China;
2. Department of Biology, University of Maryland, College Park, MD 20742, U. S. A.;
3. School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China

Received:2015-12-25 Revised:2016-03-11 Online:2016-09-01 Published:2016-09-01
Contact: Qishao LU E-mail:qishaolu@hotmail.com
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11272024, 11371046, and 11372017) and the Fundamental Research Funds for the Central Universities

摘要/Abstract

摘要：

A variety of border collision bifurcations in a three-dimensional (3D) piecewise smooth chaotic electrical circuit are investigated. The existence and stability of the equilibrium points are analyzed. It is found that there are two kinds of non-smooth fold bifurcations. The existence of periodic orbits is also proved to show the occurrence of non-smooth Hopf bifurcations. As a composite of non-smooth fold and Hopf bifurcations, the multiple crossing bifurcation is studied by the generalized Jacobian matrix. Some interesting phenomena which cannot occur in smooth bifurcations are also considered.

关键词: border collision bifurcation, multiple crossing Chinese Library Classification O, electrical circuit

Abstract:

Key words: electrical circuit, border collision bifurcation, multiple crossing Chinese Library Classification O

中图分类号:

34C23
37G10

Yinghui GAO, Xiangying MENG, Qishao LU. Border collision bifurcations in 3D piecewise smooth chaotic circuit[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(9): 1239-1250.

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Border collision bifurcations in 3D piecewise smooth chaotic circuit

Border collision bifurcations in 3D piecewise smooth chaotic circuit

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