Border Collision Bifurcations in n-Dimensional Piecewise Linear Discontinuous Maps

Dutta, Partha Sharathi; Routroy, Bitihotra; Banerjee, Soumitro; Alam, S. S.

Border Collision Bifurcations in n-Dimensional Piecewise Linear Discontinuous Maps

Authors

Dutta, Partha Sharathi

Routroy, Bitihotra

Banerjee, Soumitro

Alam, S. S.

Description

In this paper we report some important results that help in analizing 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 plane of discontinuity. Earlier, Feigin had made a similar analysis for general n-dimensional piecewise smooth continuous maps. Proceeding along similar lines, we obtain the general conditions of existence of period-1 and period-2 fixed points before and after a border collision bifurcation. The application of the method is then illustrated using a specific example of a two-dimensional discontinuous map.
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