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Higher order Melnikov analysis for planar piecewise linear vector fields with nonlinear switching curve

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Autor(es):
Andrade, Kamila da S. ; Cespedes, Oscar A. R. ; Cruz, Dayane R. ; Novaes, Douglas D.
Número total de Autores: 4
Tipo de documento: Artigo Científico
Fonte: Journal of Differential Equations; v. 287, p. 36-pg., 2021-03-29.
Resumo

In this paper, we are interested in providing lower estimations for the maximum number of limit cycles H(n) that planar piecewise linear differential systems with two zones separated by the curve y = xn can have, where n is a positive integer. For this, we perform a higher order Melnikov analysis for piecewise linear perturbations of the linear center. In particular, we obtain that H (2) >= 4, H (3) >= 8, H(n) >= 7, for n >= 4 even, and H(n) >= 9, for n >= 5 odd. This improves all the previous results for n >= 2. Our analysis is mainly based on some recent results about Chebyshev systems with positive accuracy and Melnikov Theory, which will be developed at any order for a class of nonsmooth differential systems with nonlinear switching manifold. (C) 2021 Elsevier Inc. All rights reserved. (AU)

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: 19/10269-3 - Teorias ergódica e qualitativa dos sistemas dinâmicos II
Beneficiário:Claudio Aguinaldo Buzzi
Modalidade de apoio: Auxílio à Pesquisa - Temático
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