Simultaneous Bifurcation of Limit Cycles and Critical Periods

Autor(es)

Oliveira, Regilene D. S. ^[1] ; Sanchez-Sanchez, Ivan ^[2] ; Torregrosa, Joan ^{[2, 3]}

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat, Ave Trabalhador Sao Carlense, BR-40013566 Sao Carlos, SP - Brazil

^[2] Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Catalonia - Spain

^[3] Ctr Recerca Matemat, Campus Bellaterra, Barcelona 08193 - Spain

• Tipo de documento: Artigo Científico
• Fonte: Qualitative Theory of Dynamical Systems; v. 21, n. 1 MAR 2022.
• Citações Web of Science: 0

Resumo

The present work introduces the problem of simultaneous bifurcation of limit cycles and critical periods for a system of polynomial differential equations in the plane. The simultaneity concept is defined, as well as the idea of bi-weakness in the return map and the period function. Together with the classical methods, we present an approach which uses the Lie bracket to address the simultaneity in some cases. This approach is used to find the bi-weakness of cubic and quartic Lienard systems, the general quadratic family, and the linear plus cubic homogeneous family. We finish with an illustrative example by solving the problem of simultaneous bifurcation of limit cycles and critical periods for the cubic Lienard family. (AU)

• Processo FAPESP: 19/21181-0 - Novas fronteiras na Teoria de Singularidades
• Beneficiário: Regilene Delazari dos Santos Oliveira
• Modalidade de apoio: Auxílio à Pesquisa - Temático