Hopf-like bifurcations and asymptotic stability in a class of 3D piecewise linear systems with applications
type: Item
instance of: scholarly article
title: Hopf-like bifurcations and asymptotic stability in a class of 3D piecewise linear systems with applications
zbMATH Open document ID: 1478.34015
author: Rony Cristiano
author: Mariana Q. Velter
author: Durval J. Tonon
published in: Journal of Nonlinear Science
publication date: 2021-07-29T00:00:00Z
review text: This paper analyzes a Hopf-like bifurcations in 3D piecewise linear systems, which are characterized by the birth of a piecewise smooth limit cycle that bifurcates from a singular point located at the discontinuity manifold. For a particular class of systems, it is provided the occurrence of two distinct types of Hopf-like bifurcations, each one giving rise to a crossing limit cycle. Conditions are stablished for the existence of a saddle-node bifurcation of crossing limit cycles, implying the coexistence of two crossing limit cycles. The stability property of the pseudo-equilibrium is analyzed and applications in discontinuous control systems are performed.
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 7376466
zbMATH Keywords: piecewise vector fields
zbMATH Keywords: bifurcations
zbMATH Keywords: crossing limit cycle
zbMATH Keywords: asymptotic stability
reviewed by: Douglas D. Novaes
MaRDI profile type: Publication
full work available at URL: s00332-021-09724-2
OpenAlex ID: W3164731291
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DOI: 10.1007/S00332-021-09724-2
description: scientific article; zbMATH DE number 7376466