  We present two ways of regularizing a one parameter family of piece-wise
smooth dynamical systems undergoing a codimension one grazing-sliding global
bifurcation of periodic orbits. First we use the Sotomayor-Teixeira
regularization and prove that the regularized family has a saddle-node
bifurcation of periodic orbits. Then we perform a hysteretic regularization and
show that the regularized family has chaotic dynamics. Our result shows that,
in spite that the two regularizations will give the same dynamics in the
sliding modes, when a tangency appears the hysteretic process generates chaotic
dynamics.
