A general mechanism to generate three limit cycles in planar Filippov systems with two zones |
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Authors: | Emilio Freire Enrique Ponce Francisco Torres |
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Institution: | 1. Departamento de Matemática Aplicada, Escuela Técnica Superior de Ingeniería, Avda. de los Descubrimientos, 41092?, Sevilla, Spain 2. Departamento de Matemática Aplicada, Escuela Politécnica Superior, Virgen de Africa, 7, 41011?, Sevilla, Spain
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Abstract: | Discontinuous piecewise linear systems with two zones are considered. A general canonical form that includes all the possible configurations in planar linear systems is introduced and exploited. It is shown that the existence of a focus in one zone is sufficient to get three nested limit cycles, independently on the dynamics of the another linear zone. Perturbing a situation with only one hyperbolic limit cycle, two additional limit cycles are obtained by using an adequate parametric sector of the unfolding of a codimension-two focus-fold singularity. |
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