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

• Autor(a) principal: Buzzi, C. A. [UNESP]
• Data de Publicação: 2016
• Outros Autores: Euzébio, R. D. [UNESP], Mereu, A. C.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1016/j.bulsci.2015.06.002; http://hdl.handle.net/11449/171894
• topic: Limit cycles; Malkin's bifurcation function; Non-smooth vector fields

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 R3. The approach involves the regularization process of non-smooth vector fields and a method based in the Malkin bifurcation function for C0 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 R3 and explicit a manner to obtain them by performing non-smooth perturbations in codimension one Euclidean manifolds.