Limit cycles from a monodromic infinity in planar piecewise linear systems
Freire, Emilio (Universidad de Sevilla. Departamento de Matemática Aplicada II)
Ponce, Enrique (Universidad de Sevilla. Departamento de Matemática Aplicada II)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Torres, Francisco (Universidad de Sevilla. Departamento de Matemática Aplicada II)

Date:	2021
Abstract:	Planar piecewise linear systems with two linearity zones separated by a straight line and with a periodic orbit at infinity are considered. By using some changes of variables and parameters, a reduced canonical form with five parameters is obtained. Instead of the usual Bendixson transformation to work near infinity, a more direct approach is introduced by taking suitable coordinates for the crossing points of the possible periodic orbits with the separation straight line. The required computations to characterize the stability and bifurcations of the periodic orbit at infinity are much easier. It is shown that the Hopf bifurcation at infinity can have degeneracies of co-dimension three and, in particular, up to three limit cycles can bifurcate from the periodic orbit at infinity. This provides a new mechanism to explain the claimed maximum number of limit cycles in this family of systems. The centers at infinity classification together with the limit cycles bifurcating from them are also analyzed.
Grants:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 Ministerio de Ciencia e Innovación MTM2016-77278-P Ministerio de Ciencia e Innovación MTM2017-87915-D2-1-P Ministerio de Ciencia e Innovación PGC2018-096265-B-I00 European Commission 777911
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Planar piecewise linear systems ; Bifurcation from infinity ; Limit cycles ; Centers
Published in:	Journal of mathematical analysis and applications, Vol. 496, Issue 2 (April 2021) , art. 124818, ISSN 1096-0813

DOI: 10.1016/j.jmaa.2020.124818

Postprint 24 p, 359.3 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles