Bifurcation of limit cycles from a periodic annulus formed by a center and two saddles in piecewise linear differential system with three zones

Autor(es)

Pessoa, Claudio ; Ribeiro, Ronisio

• Tipo de documento: Artigo Científico
• Fonte: NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS; v. 80, p. 17-pg., 2024-06-27.

Resumo

In this paper, we study the number of limit cycles that can bifurcate from a periodic annulus in discontinuous planar piecewise linear Hamiltonian differential system with three zones separated by two parallel straight lines, such that the linear differential systems that define the piecewise one have a center and two saddles. That is, the linear differential system in the region between the two parallel lines (called of central subsystem) has a center and the others subsystems have saddles. We prove that if the central subsystem has a real or a boundary center, then at least six limit cycles can bifurcate from the periodic annulus by linear perturbations. Four passing through the three zones and two passing through two zones. Now, if the central subsystem has a virtual center, then at leas four limit cycles can bifurcate from the periodic annulus by linear perturbations, three passing through the three zones and one passing through two zones. For this, we obtain a normal form for these piecewise Hamiltonian systems and study the number of zeros of its Melnikov functions defined in two and three zones. (AU)

• Processo FAPESP: 19/10269-3 - Teorias ergódica e qualitativa dos sistemas dinâmicos II
• Beneficiário: Claudio Aguinaldo Buzzi
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 23/04061-6 - Sistemas dinâmicos contínuos ou suaves por partes em variedades de dimensão 2 e 3.
• Beneficiário: Cláudio Gomes Pessoa
• Modalidade de apoio: Auxílio à Pesquisa - Regular