Dynamical analysis of a fold-fold regularized system of type II with reverse direction

Abstract:

Sotomayor and Teixeira proposed a method, namely S-T regularization, to regularize piecewise smooth systems. We in this paper study the dynamical behaviors of a fold-fold regularized system of type II with reverse direction. With the non-degenerate condition of divergence, we show that the equilibrium of regularized system is either a node or a focus. Moreover, we also show that the order and stability of the focus vary with the parameters and give the degenerate curve of the focus. Finally, we discuss the dependence of the order of focus on the regularized function.

Key words:Piecewise smooth system; Tangent point; Regularization; Hopf bifurcation