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Coexistence of singular cycles in a new kind of 3D non-smooth systems with two discontinuous boundaries

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Abstract

The aim here is to study complex dynamical behavior in a new kind of non-smooth systems with two discontinuous boundaries in space \(\mathbb {R}^3\). This paper provides an applicable method for accurately detecting coexistence of singular cycles, including (a) homoclinic and homoclinic cycles, (b) homoclinic and heteroclinic cycles, (c) heteroclinic and heteroclinic cycles. It is further proposed some criteria for guaranteeing three types of coexistence in the considered system. Moreover, existence conditions of chaos induced by such coexistence are established. Finally, three numerical examples are provided to verify the validity of theoretical results.

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Acknowledgements

This work was supported by the China Scholarship Council (No. 201906290182), the National Natural Science Foundation of China (No. 11901091), the Natural Science Foundation of Guangdong Province (No. 2020A151501339).

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Authors and Affiliations

  1. School of Science, Tianjin University of Commerce, Tianjin, 300134, People’s Republic of China

    Kai Lu

  2. School of Mathematics and Big Date, Foshan University, Foshan, 528000, People’s Republic of China

    Wenjing Xu & Qiaomin Xiang

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  1. Kai Lu
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  2. Wenjing Xu
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Correspondence to Wenjing Xu.

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Lu, K., Xu, W. & Xiang, Q. Coexistence of singular cycles in a new kind of 3D non-smooth systems with two discontinuous boundaries. Nonlinear Dyn 104, 149–164 (2021). https://doi.org/10.1007/s11071-021-06236-2

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  • DOI: https://doi.org/10.1007/s11071-021-06236-2

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