On the existence of low-period orbits in <Emphasis Type="Italic">n</Emphasis>-dimensional piecewise linear discontinuous maps |
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Authors: | Partha Sharathi Dutta Bitihotra Routroy Soumitro Banerjee S S Alam |
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Institution: | (1) Department of Mathematics and Centre for Theoretical Studies, Indian Institute of Technology, Kharagpur, 721302, India;(2) Department of Electrical Engineering, Indian Institute of Technology, Kharagpur, 721302, India;(3) Department of Mathematics, Indian Institute of Technology, Kharagpur, 721302, India |
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Abstract: | Discontinuous maps occur in many practical systems, and yet bifurcation phenomena in such maps is quite poorly understood.
In this paper, we report some important results that help in analyzing 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. In this paper, we extend that line of work for maps with discontinuity to 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.
This work was supported in part by the BRNS, Department of Atomic Energy (DAE), Government of India under project no. 2003/37/11/BRNS. |
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Keywords: | Border collision bifurcation Normal form Discontinuous map Periodic solutions |
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