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Border collision bifurcations in 3D piecewise smooth chaotic circuit

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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.

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Authors and Affiliations

  1. School of Mathematics and System Sciences, LMIB of the Ministry of Education, Beihang University, Beijing, 100191, China

    Yinghui Gao

  2. Department of Biology, University of Maryland, College Park, MD, 20742, USA

    Xiangying Meng

  3. School of Aeronautic Science and Engineering, Beihang University, Beijing, 100191, China

    Qishao Lu

Authors
  1. Yinghui Gao
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  2. Xiangying Meng
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  3. Qishao Lu
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Corresponding author

Correspondence to Qishao Lu.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11272024, 11371046, and 11372017) and the Fundamental Research Funds for the Central Universities

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Gao, Y., Meng, X. & Lu, Q. Border collision bifurcations in 3D piecewise smooth chaotic circuit. Appl. Math. Mech.-Engl. Ed. 37, 1239–1250 (2016). https://doi.org/10.1007/s10483-016-2129-6

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  • DOI: https://doi.org/10.1007/s10483-016-2129-6

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