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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.)

Bifurcation of limit cycles from a non-smooth perturbation of a two-dimensional isochronous cylinder

Full text
Author(s):
Buzzi, C. A. [1] ; Euzebio, R. D. [1] ; Mereu, A. C. [2]
Total Authors: 3
Affiliation:
[1] IBILCE UNESP Univ Estadual Paulista, Dept Math, Rua Cristovao Colombo 2265, BR-15054000 Selo Jose De Rio Preto, SP - Brazil
[2] Univ Fed Sao Carlos, Dept Phys Chem & Math, BR-18052780 Sorocaba, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: BULLETIN DES SCIENCES MATHEMATIQUES; v. 140, n. 5, p. 519-540, JUN 2016.
Web of Science Citations: 0
Abstract

Detect the birth of limit cycles in non-smooth vector fields is a very important matter into the recent theory of dynamical systems and applied sciences. The goal of this paper is to study the bifurcation of limit cycles from a continuum of periodic orbits filling up a two-dimensional isochronous cylinder of a vector field in R-3. The approach involves the regularization process of non-smooth vector fields and a method based in the Malkin bifurcation function for C-0 perturbations. The results provide sufficient conditions in order to obtain limit cycles emerging from the cylinder through smooth and non smooth perturbations of it. To the best of our knowledge they also illustrate the implementation by the first time of a new method based in the Malkin bifurcation function. In addition, some points concerning the number of limit cycles bifurcating from non-smooth perturbations compared with smooth ones are studied. In summary the results yield a better knowledge about limit cycles in non-smooth vector fields in R-3 and explicit a manner to obtain them by performing non-smooth perturbations in codimension one Euclidean manifolds. (C) 2015 Elsevier Masson SAS. All rights reserved. (AU)

FAPESP's process: 14/18508-3 - Minimal sets of piecewise differential systems in dimension 3
Grantee:Rodrigo Donizete Euzébio
Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
FAPESP's process: 12/18780-0 - Geometry of control systems, dynamical and stochastics systems
Grantee:Marco Antônio Teixeira
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 13/24541-0 - Ergodic and qualitative theory of dynamical systems
Grantee:Claudio Aguinaldo Buzzi
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 13/25828-1 - Minimal sets and invariant manifolds in piecewise smooth systems
Grantee:Rodrigo Donizete Euzébio
Support Opportunities: Scholarships in Brazil - Post-Doctoral