Limit cycles in planar piecewise linear differential systems with nonregular separation line
Cardin, Pedro Toniol (UNESP(Brazil). Departamento de Matemática)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2016
Abstract:	In this paper we deal with lanar piecewise linear differential systems defined in two zones. We consider the case when the two linear zones are angular sectors of angles and 2 - respectively, for (0,). We study the problem of determining lower bounds for the number of isolated periodic orbits in such systems using Melnikov functions. These limit cycles appear studying higher order piecewise linear perturbations of a linear center. It is proved that the maximum number of limit cycles that can appear up to a sixth order perturbation is five. Moreover, for these values of we prove the existence of systems with four limit cycles up to fifth order and, for =/2, we provide an explicit example with five up to sixth order. In general, the nonregular separation line increases the number of periodic orbits in comparison with the case where the two zones are separated by a straight line.
Grants:	Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 318999
Note:	Agraïments: The first author is supported by FAPESP grant number 2013/24541-0 and CAPES grant number 88881.030454/2013-01 Program CSF-PVE and UNAB13-4E-1604.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Limit cycle in Melnikov higher order perturbation ; Non-smooth differential systems in two zones ; Nonregular separation line
Published in:	Physica D. Nonlinear phenomena, Vol. 337 (2016) , p. 67-82, ISSN 0167-2789

DOI: 10.1016/j.physd.2016.07.008

Postprint 23 p, 495.5 KB

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