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Homoclinic orbits and an invariant chaotic set in a new 4D piecewise affine systems

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Abstract

It is a challenging task to prove mathematically the existence of homoclinic orbits in a high-dimensional dynamical system. Here we first introduce a new four-dimensional (4D) piecewise affine system and then establishes useful yet general conditions on the existence of an orbit homoclinic to a spiral saddle-foci and chaos in the system. Rigorously mathematical analysis is also provided. A 4D example with both a homoclinic orbit and an invariant chaotic set is used to depict the effectiveness of analysis and prediction.

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Acknowledgements

This study was supported by Natural Science Foundation of China (No. 11671149) and Natural Science Foundation of Guangdong Province (No. 2017A030312006).

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Authors and Affiliations

  1. School of Mathematics, South China University of Technology, Guangzhou, 510640, China

    Qigui Yang & Kai Lu

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  1. Qigui Yang
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  2. Kai Lu
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Correspondence to Qigui Yang.

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Yang, Q., Lu, K. Homoclinic orbits and an invariant chaotic set in a new 4D piecewise affine systems. Nonlinear Dyn 93, 2445–2459 (2018). https://doi.org/10.1007/s11071-018-4335-6

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