Limit cycles for discontinuous quadratic differential systems with two zones

In this paper we study the maximum number of limit cycles given by the averaging theory of first order for discontinuous differential systems, which can bifurcate from the periodic orbits of the quadratic isochronous centers ˙x = -y + x2, ˙y = x + xy and ˙x = -y + x2 - y2, y˙ = x + 2xy when they are...

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Detalhes bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Mereu, Ana Cristina
Formato: artículo
Fecha de publicación:2014
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:150734
Acesso em linha:https://ddd.uab.cat/record/150734
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2013.12.031
Access Level:acceso abierto
Palavra-chave:Limit cycles
Discontinuous quadratic systems
Averaging theory
Isochronous center
Descrição
Resumo:In this paper we study the maximum number of limit cycles given by the averaging theory of first order for discontinuous differential systems, which can bifurcate from the periodic orbits of the quadratic isochronous centers ˙x = -y + x2, ˙y = x + xy and ˙x = -y + x2 - y2, y˙ = x + 2xy when they are perturbed inside the class of all discontinuous quadratic polynomial differential systems with the straight line of discontinuity y = 0. Comparing the obtained results for the discontinuous with the results for the continuous quadratic polynomial differential systems, this work shows that the discontinuous systems have at least 3 more limit cycles surrounding the origin than the continuous ones.