Abstract:

We consider а two-parameter family of piecewise smooth dynamical systems on the plane. For zero values of the parameters the dynamical system has а periodic trajectory L passing through two singular points of the fork type and not containing other singular points. It is assumed that L contains both the tangent and transverse separatrices of both forks. We consider different cases of the location of the remaining separatrices. In each case, we describe bifurcations in a neighborhood of L for generic families.