Border Collision Bifurcations in n-Dimensional Piecewise Linear Discontinuous Maps
Chaotic Dynamics
2007-05-23 v2
Abstract
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.
Cite
@article{arxiv.nlin/0601038,
title = {Border Collision Bifurcations in n-Dimensional Piecewise Linear Discontinuous Maps},
author = {Partha Sharathi Dutta and Bitihotra Routroy and Soumitro Banerjee and S. S. Alam},
journal= {arXiv preprint arXiv:nlin/0601038},
year = {2007}
}
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