Border collision bifurcations in n-dimensional piecewise linear discontinuous maps

Abstract

In this paper we make a first attempt to present a systematic classification and analysis of the border collision bifurcations that occur in n-dimensional discontinuous maps. For this purpose, we use the piecewise linear approximation in the neighborhood of the planes of discontinuity. Following Feigin's approach (which he used for continuous maps) we obtain some important results applicable for piecewise linear discontinuous maps of arbitrary dimension. The application of the method is then illustrated using a specific example of a 2-dimensional discontinuous map.