Limit cycles for discontinuous quadratic differential systems with two zones

Autor(es)

Llibre, Jaume ^[1] ; Mereu, Ana C. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia - Spain

^[2] Univ Fed Sao Carlos, Dept Phys Chem & Math, BR-18052780 Sorocaba, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Analysis and Applications; v. 413, n. 2, p. 763-775, MAY 15 2014.
• Citações Web of Science: 34

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) over dot = -y + x(2), (y) over dot = x + xy and (x) over dot = -y + x(2) - y(2), (y) over dot = 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. (C) 2013 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 12/20884-8 - Órbitas periódicas em sistemas descontínuos
• Beneficiário: Ana Cristina de Oliveira Mereu
• Modalidade de apoio: Bolsas no Exterior - Pesquisa