A general mechanism to generate three limit cycles in planar Filippov systems with two zones

作者：Freire Emilio; Ponce Enrique^*; Torres Francisco

来源：Nonlinear Dynamics, 2014, 78(1): 251-263.

DOI：10.1007/s11071-014-1437-7

• Discontinuous piecewise linear systems
• Lienard equation
• Limit cycles

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.

• 出版日期2014-10