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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.)

Limit Cycles Bifurcating from the Periodic Orbits of a Discontinuous Piecewise Linear Differentiable Center with Two Zones

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Author(s):
Llibre, Jaume [1] ; Novaes, Douglas D. [2] ; Teixeira, Marco A. [2]
Total Authors: 3
Affiliation:
[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia - Spain
[2] Univ Estadual Campinas, Dept Matemat, BR-13083859 Sao Paulo - Brazil
Total Affiliations: 2
Document type: Journal article
Source: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS; v. 25, n. 11 OCT 2015.
Web of Science Citations: 8
Abstract

We study a class of discontinuous piecewise linear differential systems with two zones separated by the straight line x = 0. In x > 0, we have a linear saddle with its equilibrium point living in x > 0, and in x < 0 we have a linear differential center. Let p be the equilibrium point of this linear center, when p lives in x < 0, we say that it is real, and when p lives in x > 0 we say that it is virtual. We assume that this discontinuous piecewise linear differential system formed by the center and the saddle has a center q surrounded by periodic orbits ending in a homoclinic orbit of the saddle, independent if p is real, virtual or p is in x = 0. Note that q = p if p is real or p is in x = 0. We perturb these three classes of systems, according to the position of p, inside the class of all discontinuous piecewise linear differential systems with two zones separated by x = 0. Let N be the maximum number of limit cycles which can bifurcate from the periodic solutions of the center q with these perturbations. Our main results show that N = 2 when p is on x = 0, and N >= 2 when p is a real or virtual center. Furthermore, when p is a real center we found an example satisfying N >= 3. (AU)

FAPESP's process: 13/16492-0 - Averaging Theory for studying the periodic solutions of the differential systems and its applications
Grantee:Douglas Duarte Novaes
Support type: Scholarships abroad - Research Internship - Doctorate
FAPESP's process: 12/18780-0 - Geometry of control systems, dynamical and stochastics systems
Grantee:Marco Antônio Teixeira
Support type: Research Projects - Thematic Grants