Limit cycles via higher order perturbations for some piecewise differential systems
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....
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:199355 |
| Acesso em linha: | https://ddd.uab.cat/record/199355 https://dx.doi.org/urn:doi:10.1016/j.physd.2018.01.007 |
| Access Level: | acceso abierto |
| Palavra-chave: | Liénard piecewise differential system Limit cycle in Melnikov higher order perturbation Non-smooth differential system |
| Resumo: | 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. |
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