Limit cycles in piecewise polynomial systems allowing a non-regular switching boundary
Li, Tao (Sichuan University. Department of Mathematics (China))
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2021
Abstract:	Continuing the investigation for the piecewise polynomial perturbations of the linear center ẋ = −y, ẏ = x from Buzzi et al. (2018) for the case where the switching boundary is a straight line, in this paper we allow that the switching boundary is non-regular, i. e. we consider a switching boundary which separates the plane into two angular sectors with angles α ∈ (0,π] and 2π − α. Moreover, unlike the aforementioned work, we allow that the polynomial differential systems in the two sectors have different degrees. Depending on α and for arbitrary given degrees we provide an upper bound for the maximum number of limit cycles that bifurcate from the periodic orbits of the linear center using the averaging method up to any order. This upper bound is reached for the first two orders. On the other hand, we pay attention to the perturbation of the linear center inside this class of piecewise polynomial Liénard systems and give some better upper bounds in comparison with the one obtained in the general piecewise polynomial perturbations. Again our results imply that the non-regular switching boundary (i. e. when α ≠ π) of the piecewise polynomial perturbations usually leads to more limit cycles than the regular case (i. e. when α = π) where the switching boundary is a straight line.
Grants:	Ministerio de Ciencia e Innovación MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 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:	Averaging method ; Hilbert's 16th problem ; Limit cycles ; Discontinuous piecewise polynomial systems ; Liénard systems
Published in:	Physica D. Nonlinear phenomena, Vol. 419 (May 2021) , p. 132855, ISSN 0167-2789

DOI: 10.1016/j.physd.2021.132855

Postprint 26 p, 910.3 KB

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