Melnikov analysis in nonsmooth differential systems with nonlinear switching manifold

Autor(es)

Bastos, Jefferson L. R. ^[1] ; Buzzi, Claudio A. ^[1] ; Llibre, Jaume ^[2] ; Novaes, Douglas D. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Estadual Paulista, UNESP, IBILCE, Av Cristovao Colombo 2265, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

^[2] UAB, Edif C Fac Ciencies, Barcelona 08193 - Spain

^[3] Univ Estadual Campinas, IMECC, UNICAMP, R Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 267, n. 6, p. 3748-3767, SEP 5 2019.
• Citações Web of Science: 0

Resumo

We study the family of piecewise linear differential systems in the plane with two pieces separated by a cubic curve. Our main result is that 7 is a lower bound for the Hilbert number of this family. In order to get our main result, we develop the Melnikov functions for a class of nonsmooth differential systems, which generalizes, up to order 2, some previous results in the literature. Whereas the first order Melnikov function for the nonsmooth case remains the same as for the smooth one (i.e. the first order averaged function) the second order Melnikov function for the nonsmooth case is different from the smooth one (i.e. the second order averaged function). We show that, in this case, a new term depending on the jump of discontinuity and on the geometry of the switching manifold is added to the second order averaged function. (C) 2019 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 16/11471-2 - Órbitas deslizantes em sistemas dinâmicos descontínuos: soluções periódicas, conexões homoclínicas, e modos não lineares de deslize
• Beneficiário: Douglas Duarte Novaes
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 18/16430-8 - Dinâmica global das equações diferenciais não suaves
• Beneficiário: Douglas Duarte Novaes
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 13/24541-0 - Teorias ergódica e qualitativa dos sistemas dinâmicos
• Beneficiário: Claudio Aguinaldo Buzzi
• Modalidade de apoio: Auxílio à Pesquisa - Temático