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

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Border collision bifurcations in 3D piecewise smooth chaotic circuit

Yinghui GAO1, Xiangying MENG2, Qishao LU3   

  1. 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

Abstract:

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.

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

2010 MSC Number: 

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