Affiliation:
1. Fujian Province University Key Laboratory of Computational Science, School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, P. R. China
Abstract
In this paper, we study bifurcations of the regularized systems of planar piecewise smooth systems, which have a visible fold-regular point and a sliding or grazing heteroclinic loop. Our results show that if the planar piecewise smooth system with a sliding heteroclinic loop undergoes sliding heteroclinic bifurcation, then the regularized system can bifurcate with a stable limit cycle passing through the regularized region and at most two limit cycles outside the regularized region. The regularized system can have at most three periodic orbits. When the upper subsystem is a Hamiltonian system, the regularized system can bifurcate with a semi-stable periodic orbit. Finally, we discuss two cases when the heteroclinic loop of a piecewise smooth system remains unbroken under a small perturbation. Our results show that the regularized system can bifurcate at most two limit cycles from an inner unstable grazing heteroclinic loop.
Funder
Quanzhou High-Level Talents Support Plan
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)
Cited by
1 articles.
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