Border Collision Bifurcations in n-Dimensional Piecewise Linear Discontinuous Maps

摘要

In this paper we report some important results that help in analizing theborder collision bifurcations that occur in n-dimensional discontinuous maps.For this purpose, we use the piecewise linear approximation in the neighborhoodof the plane of discontinuity. Earlier, Feigin had made a similar analysis forgeneral n-dimensional piecewise smooth continuous maps. Proceeding alongsimilar lines, we obtain the general conditions of existence of period-1 andperiod-2 fixed points before and after a border collision bifurcation. Theapplication of the method is then illustrated using a specific example of atwo-dimensional discontinuous map.