Computational techniques to locate crossing/sliding regions and their sets of attraction in non-smooth dynamical systems

Several models in the applied sciences are characterized by instantaneous changes in the solutions or discontinuities in the vector field. Knowledge of the geometry of interaction of the flow with the discontinuities can give new insights on the behaviour of such systems. Here, we focus on the class of the piecewise smooth systems of Filippov type. We describe some numerical techniques to locate crossing and sliding regions on the discontinuity surface, to compute the sets of attraction of these regions together with the mathematical form of the separatrices of such sets. Some numerical tests will illustrate our approach.