Piecewise smooth vector fields in ℝ3 at infinity

Abstract

In this work we study the dynamics at infinity of a piecewise smooth vector fields in ℝ3. We provide conditions for the 24-parameter family to undergo a local bifurcations of codimension zero and one at infinity. These results can be useful to understand the global dynamics of piecewise smooth vector fields. In addition, we apply our results to two families of systems from control theory, in one of them studying the existence of limit cycles at infinity.