Study of Periodic Orbits in Periodic Perturbations of Planar Reversible Filippov Systems Having a Twofold Cycle

Autor(es)

Novaes, Douglas D. ^[1] ; Seara, Tere M. ^[2] ; Teixeira, Marco A. ^[1] ; Zeli, Iris O. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Matemat, BR-13083859 Campinas, SP - Brazil

^[2] Univ Politecn Cataluna, Matemat Apliacada 1, Barcelona 08028 - Spain

^[3] Inst Tecnol Aeronaut, Div Ciencias Fundamentais, Dept Matemat, BR-12228900 Sao Jose Dos Campos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS; v. 19, n. 2, p. 1343-1371, 2020.
• Citações Web of Science: 0

Resumo

We study the existence of periodic solutions in a class of planar Filippov systems obtained from non-autonomous periodic perturbations of reversible piecewise smooth differential systems. It is assumed that the unperturbed system presents a simple twofold cycle, which is characterized by a closed trajectory connecting a visible twofold singularity to itself. It is shown that under certain generic conditions the perturbed system has sliding and crossing periodic solutions. In order to get our results, Melnikov's ideas are applied together with tools from the geometric singular perturbation theory. Finally, a study of a perturbed piecewise Hamiltonian model is performed. (AU)

• Processo FAPESP: 18/13481-0 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Marco Antônio Teixeira
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 13/21078-8 - Soluções periódicas para Sistemas Dinâmicos Descontínuos com simetria
• Beneficiário: Iris de Oliveira Zeli
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado
• Processo FAPESP: 19/10269-3 - Teorias ergódica e qualitativa dos sistemas dinâmicos II
• Beneficiário: Claudio Aguinaldo Buzzi
• Modalidade de apoio: Auxílio à Pesquisa - Temático