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On the existence of heteroclinic cycles in some class of 3-dimensional piecewise affine systems with two switching planes

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Abstract

Since complicated dynamical behavior can occur easily near homoclinic trajectory or heteroclinic cycle in dynamical systems with dimension not less than three, this paper investigates the existence of heteroclinic cycles in some class of 3-dimensional three-zone piecewise affine systems with two switching planes. Based on the exact determination of the stable manifold, unstable manifold and analytic solution, a rigorous analytic methodology of designing chaos generators is proposed, which may be of potential applications to chaos secure communication. Furthermore, we obtain three sufficient conditions for the existence of a single or two heteroclinic cycles in three different cases. Finally, some examples are given to illustrate our theoretical results.

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Acknowledgements

The authors are grateful to the editors and the anonymous reviewers for their careful reading and insightful suggestions. This work is partially supported by the National Natural Science Foundation of China (11472111), and the second author is supported by the National Natural Science Foundation of China (11702077).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China

    Yanli Chen & Xiao-Song Yang

  2. School of Mathematics, Yibin University, Yibin, 644007, China

    Yanli Chen

  3. Department of Mathematics and Physics, Hefei University, Hefei, 230601, China

    Lei Wang

  4. Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, China

    Xiao-Song Yang

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  1. Yanli Chen
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  2. Lei Wang
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Correspondence to Xiao-Song Yang.

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Chen, Y., Wang, L. & Yang, XS. On the existence of heteroclinic cycles in some class of 3-dimensional piecewise affine systems with two switching planes. Nonlinear Dyn 91, 67–79 (2018). https://doi.org/10.1007/s11071-017-3856-8

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  • DOI: https://doi.org/10.1007/s11071-017-3856-8

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