Limit cycles via higher order perturbations for some piecewise differential systems
Buzzi, Claudio. (Universidade Estadual Paulista (Brasil). Department of Mathematics)
Lima, Mauricio Firmino Silva (Universidade Federal do ABC(Brazil). Centro de Matemática Computacâo e Cognicâo)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Data:	2018
Resum:	A classical perturbation problem is the polynomial perturbation of the harmonic oscillator, (x',y')=(-y + εf(x,y,ε),x εg(x,y,ε)). In this paper we study the limit cycles that bifurcate from the period annulus via piecewise polynomial perturbations in two zones separated by a straight line. We prove that, for polynomial perturbations of degree n, no more than Nn-1 limit cycles appear up to a study of order N. We also show that this upper bound is reached for orders one and two. Moreover, we study this problem in some classes of piecewise Li\'enard differential systems. When we restrict the analysis to some special class this upper bound never is attained and we show which is this upper bound for higher order perturbation in . The Poincar\'e--Pontryagin--Melnikov theory is the main technique used to prove all the results.
Ajuts:	European Commission 318999 European Commission 316338 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
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Liénard piecewise differential system ; Limit cycle in Melnikov higher order perturbation ; Non-smooth differential system
Publicat a:	Physica D. Nonlinear phenomena, Vol. 371 (May 2018) , p. 28-47, ISSN 0167-2789

DOI: 10.1016/j.physd.2018.01.007

Postprint 38 p, 502.2 KB

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