On the Interior Crisis in a Pulse Modulated Control System

In this paper we discuss a global bifurcation associated with the interior crisis that one can observe in the model of a pulse control system. As concrete example of the system that can demonstrate such a phenomenon we consider a DC motor drive with pulse-width modulated control. The behavior of such a system is described by two dimensional nonautonomous differential equations. This model is reduced to the two-dimensional non-smooth continuous map. The paper contains detailed numerical calculations of the phase portraits that are illustrated main stages of the interior crisis in the dynamics of the considered control system. We show that this phenomenon is appeared in a homoclinic bifurcation a saddle cycle which is located on the boundary of the basin of attraction for a chaotic motion. The presented results play important role for the prediction, detection of irregular regimes and control of oscillations in nonlinear pulse systems.