Bifurcation of limit cycles from an n-dimensional linear center inside a class of piecewise linear differential systems

Author(s)

Cardin, Pedro Toniol ^[1] ; de Carvalho, Tiago ^[1] ; Llibre, Jaume ^[2]

Affiliation

^[1] IBILCE UNESP, BR-15054000 Sao Paulo - Brazil

^[2] Univ Autonoma Barcelona, Dept Matemat, Barcelona 08913, Catalonia - Spain

• Document type: Journal article
• Source: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS; v. 75, n. 1, p. 143-152, JAN 2012.
• Web of Science Citations: 6

Abstract

Let n be an even integer. We study the bifurcation of limit cycles from the periodic orbits of the n-dimensional linear center given by the differential system <(x)over dot>(1) = -x(2), <(x)over dot>(2) = x(1), ... , <(x)over dot>(n-1) = -x(n), <(x)over dot>(n) = x(n-1), perturbed inside a class of piecewise linear differential systems. Our main result shows that at most (4n - 6)(n/2-1) limit cycles can bifurcate up to first-order expansion of the displacement function with respect to a small parameter. For proving this result we use the averaging theory in a form where the differentiability of the system is not needed. (C) 2011 Elsevier Ltd. All rights reserved. (AU)

• FAPESP's process: 07/07957-8 - Differential equations with impasses and singular perturbation
• Grantee: Pedro Toniol Cardin
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 07/08707-5 - Study of minimal sets for discontinuous systems via singular perturbations
• Grantee: Tiago de Carvalho
• Support Opportunities: Scholarships in Brazil - Doctorate