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Bifurcations of a Generalized Heteroclinic Loop in a Planar Piecewise Smooth System with Periodic Perturbations

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Abstract

This work deals with the periodic orbit bifurcations of a T-periodic perturbed piecewise smooth system whose unperturbed part has a generalized heteroclinic loop connecting a hyperbolic critical point and a quadratic tangential singularity. By constructing several displacement functions that depend on perturbation parameter \(\varepsilon \) and time t, sufficient conditions of the existence of a homoclinic loop and a sliding generalized heteroclinic loop (that is a generalized heteroclinic loop a part of which lies on the switching manifold) are obtained. As the application, we give a concrete example to show that under suitable perturbations of the generalized heteroclinic loop the corresponding phenomena can appear.

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The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 12171056), the Natural Science Foundation of Hunan Province, China (Grant No. 2021JJ30698), and the Research Foundation of Education Bureau of Hunan Province, China(Grant No. 20B018).

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Authors and Affiliations

  1. School of Mathematics, Hunan University, Changsha, 410082, Hunan, People’s Republic of China

    Fang Wu

  2. College of Mathematics and Computer Science, Changsha University, Changsha, 410022, Hunan, People’s Republic of China

    Lihong Huang

  3. School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, 410114, Hunan, People’s Republic of China

    Lihong Huang & Jiafu Wang

Authors
  1. Fang Wu
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  2. Lihong Huang
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  3. Jiafu Wang
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Correspondence to Lihong Huang.

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Wu, F., Huang, L. & Wang, J. Bifurcations of a Generalized Heteroclinic Loop in a Planar Piecewise Smooth System with Periodic Perturbations. Qual. Theory Dyn. Syst. 21, 29 (2022). https://doi.org/10.1007/s12346-021-00554-x

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