Limit cycles via higher order perturbations for some piecewise differential systems
| Autor: | Maurício Firmino Silva Lima, Claudio A. Buzzi, Joan Torregrosa |
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| Přispěvatelé: | Universidade Estadual Paulista (Unesp), Universidade Federal do ABC (UFABC), Univ Autonoma Barcelona |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Physics
Non-smooth differential system 010102 general mathematics Mathematical analysis Perturbation (astronomy) Statistical and Nonlinear Physics Condensed Matter Physics Differential systems 01 natural sciences Upper and lower bounds 010101 applied mathematics Liénard piecewise differential system Limit cycle in Melnikov higher order perturbation Lienard piecewise differential system Piecewise 0101 mathematics Harmonic oscillator |
| Zdroj: | Web of Science Repositório Institucional da UNESP Universidade Estadual Paulista (UNESP) instacron:UNESP Dipòsit Digital de Documents de la UAB Universitat Autònoma de Barcelona Recercat. Dipósit de la Recerca de Catalunya instname Recercat: Dipósit de la Recerca de Catalunya Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Popis: | Made available in DSpace on 2018-11-26T17:49:14Z (GMT). No. of bitstreams: 0 Previous issue date: 2018-05-15 MINECO AGAUR grant European Community grants Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) A classical perturbation problem is the polynomial perturbation of the harmonic oscillator, (x', y') = (-y + epsilon f(x, y, epsilon), x + epsilon g(x, y, epsilon)). 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 Lienard differential systems providing better upper bounds for higher order perturbation in 8, showing also when they are reached. The Poincare-Pontryagin-Melnikov theory is the main technique used to prove all the results. (C) 2018 Elsevier B.V. All rights reserved. Univ Estadual Paulista, Dept Matemat, Sao Jose Do Rio Preto, Brazil Univ Fed ABC, Ctr Matemat Comp & Cognicao, BR-09210170 Santo Andre, SP, Brazil Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain Univ Estadual Paulista, Dept Matemat, Sao Jose Do Rio Preto, Brazil MINECO: MTM2013-40998-P MINECO: MTM2016-77278-P AGAUR grant: 2014 SGR568 European Community grants: FP7-PEOPLE-2012-IRSES 316338 European Community grants: 318999 FAPESP: 2012/18780-0 FAPESP: 2013/24541-0 FAPESP: 2017/03352-6 |
| Databáze: | OpenAIRE |
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