LIMIT CYCLES OF DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS

Autor(es)

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

Afiliação do(s) autor(es)

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

^[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona - Spain

• Tipo de documento: Artigo Científico
• Fonte: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS; v. 21, n. 11, p. 3181-3194, NOV 2011.
• Citações Web of Science: 2

Resumo

We study the bifurcation of limit cycles from the periodic orbits of a two-dimensional (resp. four-dimensional) linear center in R(n) perturbed inside a class of discontinuous piecewise linear differential systems. Our main result shows that at most 1 (resp. 3) limit cycle can bifurcate up to first-order expansion of the displacement function with respect to the small parameter. This upper bound is reached. For proving these results, we use the averaging theory in a form where the differentiability of the system is not needed. (AU)

• Processo FAPESP: 07/07957-8 - Equações diferenciais com impasses e perturbações singulares
• Beneficiário: Pedro Toniol Cardin
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 07/08707-5 - Estudo de conjuntos minimais para sistemas descontínuos via perturbações singulares
• Beneficiário: Tiago de Carvalho
• Modalidade de apoio: Bolsas no Brasil - Doutorado