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

Wu, Fang ^[1] ; Huang, Lihong ^[2] ; Wang, Jiafu ^[2]
1. [1] Hunan University
  
  Hunan University
  
  China
2. [2] Changsha University of Science and Technology
  
  Changsha University of Science and Technology
  
  China
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 2, 2022
Idioma: inglés
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Resumen
- 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 ε 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.