About Limit Cycles in Continuous Piecewise Linear Differential Systems

Maurício Firmino Silva Lima, Claudio Pessoa, Weber Pereira

Resumo


In 2012, Lima and Llibre in [3] have studied a class of planar continuous piecewise linear vector fields with three zones. This class can be separated in four other classes and they proved, using the Poincaré map, that this particular class admits always a unique hyperbolic limit cycle. Here, we extended this study for other classes. We proved that some of them also admit always a unique hyperbolic limit cycle, moreover, we find a class that does not have limit cycles and prove the appearance of two limit cycles with one of these cycles appear by perturbations of a period annulus.


Palavras-chave


piecewise linear vector fields, Poincaré map, limit cycles, center, focus.

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DOI: https://doi.org/10.5540/03.2017.005.01.0028

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