Limit cycles of piecewise polynomial perturbations of higher dimensional lineal differential systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Novaes, Douglas D. (Universidade Estadual de Campinas. Departamento de Matemática (Brazil))
Zeli, Iris O. (Instituto Tecnológico de Aeronáutica. Departamento de Matemática (Brazil))

Date:	2020
Abstract:	The averaging theory has been extensively employed for studying periodic solutions of smooth and nonsmooth differential systems. Here, we extend the averaging theory for studying periodic solutions a class of regularly perturbed non-autonomous n-dimensional discontinuous piecewise smooth differential system. As a fundamental hypothesis, it is assumed that the unperturbed system has a manifold Z ⊂ Rn of periodic solutions satisfying dim(Z) < n. Then, we apply this result to study limit cycles bifurcating from periodic solutions of linear differential systems, x0 = Mx, when they are perturbed inside a class of discontinuous piecewise polynomial differential systems with two zones. More precisely, we study the periodic solutions of the following differential system x0 = Mx + εFn 1 (x) + ε2Fn 2 (x), in Rd+2 where ε is a small parameter, M is a (d+2)×(d+2) matrix having one pair of pure imaginary conjugate eigenvalues, m zeros eigenvalues, and d−m non-zero real eigenvalues.
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 2009/SGR-0410
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Averaging method ; Filippov system ; Limit cycle ; Nonsmooth dynamical system ; Nonsmooth polynomial differential systems ; Periodic orbit ; Polynomial differential system
Published in:	Revista Matemática Iberoamericana, Vol. 36, Núm. 1 (2020) , p. 291-318, ISSN 0213-2230

DOI: 10.4171/rmi/1131

Postprint 31 p, 575.7 KB

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