Universidad de Sevilla
Exploiting the features of a linear boundary focus in getting limit cycles
Within the realm of planar piecewise smooth differential systems or Filippov systems, the appearance of a boundary focus under parameter variations can lead to a handful of bifurcations. We show how the special features of this singular point can be exploited to justify the existence of three limit cycles in planar Filippov systems whose discontinuous vector field is defined through two linear systems. This is a joint work with Emilio Freire and Francisco Torres; see E. Freire, E. Ponce and F. Torres, A general mechanism to generate three limit cycles in planar Filippov systems with two zones, Nonlinear Dynamics (2014) 78:251–263.