Multiple attractor bifurcation in a piecewise-smooth map with quasiperiodicity

Zhusubaliyev, Zhanybai T. ; Soukhoterin, Evgeniy ; Mosekilde, Erik ; Banerjee, Soumitro (2006) Multiple attractor bifurcation in a piecewise-smooth map with quasiperiodicity 1st IFAC Conference on Analysis and Control of Chaotic Systems, 1 (1). ISSN 1474-6670

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Official URL: http://www.ifac-papersonline.net/Detailed/29995.ht...

Related URL: http://dx.doi.org/10.3182/20060628-3-FR-3903.00076

Abstract

It is known that border-collision bifurcations in piecewise-smooth maps can lead to situations where several attractors are created simultaneously in so-called "multiple attractor" or "multiple choice" bifurcations. Phenomena of this type have also been observed in various physical and technical systems. We have recently demonstrated that piecewise-smooth systems can exhibit a new type of border-collision bifurcations in which a stable invariant curve, associated with a quasiperiodic or a periodic orbit, arises from a fixed point. In this paper we consider a particular variant of the multiple attractor bifurcation in which a stable periodic cycle arises simultaneously with a closed invariant curve. We also show examples of simultaneously appearing stable periodic orbits and of the simultaneous generation of periodic and chaotic attractors.

Item Type:Article
Source:Copyright of this article belongs to International Federation of Automatic Control.
ID Code:81386
Deposited On:06 Feb 2012 04:17
Last Modified:06 Feb 2012 04:17

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