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On the existence of homoclinic orbits in some class of three-dimensional piecewise affine systems

Abstract

In this paper, we investigate a class of three-dimensional piecewise affine systems with the matrix in each subsystem processing a pair of complex eigenvalues and a real eigenvalue. Furthermore, we obtain some sufficient and necessary conditions for the existence of homoclinic orbits under suitable assumptions. Finally, some concrete examples are presented to illustrate our results.

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Acknowledgements

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

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Correspondence to Xiaosong Yang.

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Communicated by Maria do Rosário de Pinho.

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Chen, Y., Wu, T. & Yang, X. On the existence of homoclinic orbits in some class of three-dimensional piecewise affine systems. Comp. Appl. Math. 37, 6022–6033 (2018). https://doi.org/10.1007/s40314-018-0659-6

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  • DOI: https://doi.org/10.1007/s40314-018-0659-6

Keywords

  • Homoclinic orbit
  • Chaos
  • Piecewise affine systems

Mathematics Subject Classification

  • 37D45
  • 37G20