Periodic orbits for planar piecewise smooth systems with a line of discontinuity
type: Item
instance of: scholarly article
title: Periodic orbits for planar piecewise smooth systems with a line of discontinuity
zbMATH Open document ID: 1320.34063
published in: Journal of Dynamics and Differential Equations
publication date: 2015-01-23T00:00:00Z
review text: The paper deals with bifurcation phenomena in the context of Filipov's theory for discontinuous planar systems of ODEs. More precisely, the study is mainly focused on the investigation of the following family of piecewise linear systems: \[ \dot{u}= A_1u,\text{ if }y-qx-m<0\text{ and }\dot{u}= A_2u\text{ when }y-qx-m>0, \] where \(u=(x,y)^T\in \mathbb{R}^2\), \(A_1,A_2\) are \(2\times2\) matrices with constant coefficients and complex conjugate eigenvalues. The existence of periodic orbits is examined. The distance from the equilibrium \(u=0\) to the line of dicontinuity \(y-qx-m=0\) plays the role of a bifurcation parameter. Finally, the results are extended for a weak non linear perturbation of the system.
reviewed by: Tihomir Gyulov
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 34C29
zbMATH DE Number: 6389985
zbMATH Keywords: piecewise smooth systems
zbMATH Keywords: periodic orbits
zbMATH Keywords: bifurcation
zbMATH Keywords: Filippov
zbMATH Keywords: Hopf
author: Luca Dieci
author: Cinzia Elia
MaRDI profile type: Publication
full work available at URL: s10884-014-9380-3
OpenAlex ID: W2160510685
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DOI: 10.1007/S10884-014-9380-3
description: scientific article; zbMATH DE number 6389985