Limit cycles of piecewise smooth differential equations on two dimensional torus
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Miranda Martins, Ricardo (Universidade Estadual de Campinas. Instituto de Matemática, Estatística e Computação Científica)
Tonon, Durval José (Universidade Federal de Goiás. Instituto de Matemática e Estatística)

Date:	2018
Abstract:	In this paper we study the limit cycles of some classes of piecewise smooth vector fields defined in the two dimensional torus. The piecewise smooth vector fields that we consider are composed by linear, Ricatti with constant coefficients and perturbations of these one, which are given in (3). Considering these piecewise smooth vector fields we characterize the global dynamics, studying the upper bound of number of limit cycles, the existence of non-trivial recurrence and a continuum of periodic orbits. We also present a family of piecewise smooth vector fields that posses a finite number of fold points and, for this family we prove that for any 2k number of limit cycles there exists a piecewise smooth vector fields in this family that presents k number of limit cycles and prove that some classes of piecewise smooth vector fields presents a non-trivial recurrence or a continuum of periodic orbits.
Grants:	Ministerio de Economía y Competitividad MTM2016-77278-P Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 318999
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Piecewise smooth differential equations ; Limit cycles ; Global dynamics in torus
Published in:	Journal of dynamics and differential equations, Vol. 30, Issue 3 (September 2018) , p. 1011-1027, ISSN 1572-9222

DOI: 10.1007/s10884-017-9584-4

Postprint 16 p, 2.3 MB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
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