Border collision bifurcations at the change of state-space dimension

Abstract

We present the theory of border collision bifurcation for the special case where the state space is piecewise smooth, but two-dimensional in one side of the borderline, and one dimensional in the other side. This situation occurs in a class of switching circuits widely used in power electronic industry. We analyze this particular class of bifurcations in terms of the normal form, where the determinant of the Jacobian matrix at one side of the borderline is greater than unity in magnitude, and in the other side it is zero.