Degenerate grazing-sliding bifurcations in planar Filippov systems
type: Item
instance of: scholarly article
title: Degenerate grazing-sliding bifurcations in planar Filippov systems
zbMATH Open document ID: 1454.34030
author: Tao Li
author: Xingwu Chen
published in: Journal of Differential Equations
publication date: 2020-10-13T00:00:00Z
review text: This paper studies a class of degenerate grazing-sliding bifurcations of piecewise planar differential systems, whose unperturbed system has a generalized homoclinic loop to a fold-fold point. According to differential types of fold-fold points, the authors exhibit some codimension-2 bifurcation diagrams together with the asymptotics of all bifurcation curves. This work reveals several complete unfoldings of degenerate grazing-sliding bifurcations. As a consequence, they answer the problem posed in [\textit{F. Liang} et al., ibid. 255, No. 12, 4403--4436 (2013; Zbl 1301.34055)] on the maximum number of limit cycles bifurcating from the generalized homoclinic loop in case of fold-fold point.
reviewed by: Xiang Zhang
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34C07
zbMATH DE Number: 7260140
zbMATH Keywords: piecewise planar differential system
zbMATH Keywords: fold-fold point
zbMATH Keywords: grazing-sliding bifurcation
zbMATH Keywords: limit cycle
MaRDI profile type: Publication
full work available at URL: j.jde.2020.08.037
OpenAlex ID: W3089267081
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DOI: 10.1016/J.JDE.2020.08.037
description: scientific article; zbMATH DE number 7260140