Year: 2020
Author: Qiwen Xiu, Dingheng Pi
Annals of Applied Mathematics, Vol. 36 (2020), Iss. 3 : pp. 282–308
Abstract
In this paper, we consider a planar piecewise smooth differential system consisting of a linear system and a quadratic Hamiltonian system. The quadratic system has some folds on the discontinuity line. The linear system may have a focus, saddle or node. Our results show that this piecewise smooth differential system will have two limit cycles and a sliding cycle. Moreover, this piecewise smooth system will undergo pseudo-homoclinic bifurcation, Hopf bifurcation and critical crossing bifurcation $CC$. Some examples are given to illustrate our results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2020-AAM-18594
Annals of Applied Mathematics, Vol. 36 (2020), Iss. 3 : pp. 282–308
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: piecewise smooth systems limit cycle sliding cycle pseudo-homoclinic bifurcation critical crossing bifurcation $CC$.