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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Melnikov analysis in nonsmooth differential systems with nonlinear switching manifold

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Author(s):
Bastos, Jefferson L. R. [1] ; Buzzi, Claudio A. [1] ; Llibre, Jaume [2] ; Novaes, Douglas D. [3]
Total Authors: 4
Affiliation:
[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
Total Affiliations: 3
Document type: Journal article
Source: Journal of Differential Equations; v. 267, n. 6, p. 3748-3767, SEP 5 2019.
Web of Science Citations: 0
Abstract

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)

FAPESP's process: 16/11471-2 - Sliding motion in discontinuous dynamical systems: periodic solutions, homoclinic connections, and nonlinear sliding modes
Grantee:Douglas Duarte Novaes
Support type: Regular Research Grants
FAPESP's process: 18/16430-8 - Global dynamics of nonsmooth differential equations
Grantee:Douglas Duarte Novaes
Support type: Regular Research Grants
FAPESP's process: 13/24541-0 - Ergodic and qualitative theory of dynamical systems
Grantee:Claudio Aguinaldo Buzzi
Support type: Research Projects - Thematic Grants