Rakshit, Biswambhar ; Apratim, Manjul ; Banerjee, Soumitro (2010) Bifurcation phenomena in two-dimensional piecewise smooth discontinuous maps Chaos, 20 (3). 033101_1-033101_12. ISSN 1054-1500
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Official URL: http://chaos.aip.org/chaoeh/v20/i3/p033101_s1?isAu...
Related URL: http://dx.doi.org/10.1063/1.3422475
Abstract
In recent years the theory of border collision bifurcations has been developed for piecewise smooth maps that are continuous across the border and has been successfully applied to explain nonsmooth bifurcation phenomena in physical systems. However, there exist a large number of switching dynamical systems that have been found to yield two-dimensional piecewise smooth maps that are discontinuous across the border. In this paper we present a systematic approach to the problem of analyzing the bifurcation phenomena in two-dimensional discontinuous maps, based on a piecewise linear approximation in the neighborhood of the border. We first motivate the analysis by considering the bifurcations occurring in a familiar physical system-the static VAR compensator used in electrical power systems-and then proceed to formulate the theory needed to explain the bifurcation behavior of such systems. We then integrate the observed bifurcation phenomenology of the compensator with the theory developed in this paper. This theory may be applied similarly to other systems that yield two-dimensional discontinuous maps.
Item Type: | Article |
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Source: | Copyright of this article belongs to American Institute of Physics. |
Keywords: | Bifurcation; Chaos; Nonlinear Dynamical Systems; Static VAr Compensators |
ID Code: | 21397 |
Deposited On: | 20 Nov 2010 12:58 |
Last Modified: | 17 May 2016 05:37 |
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