Basins of attraction for cascading maps

Details Basins of attraction for cascading maps Basins of attraction for cascading maps

2004-08-24

arxiv.org/abs/math/0408340v1

Mathematics

Dynamical Systems

15 pages, 9 figures. To appear in International Journal of Bifurcations and Chaos

Scientific paper

We study a finite uni-directional array of "cascading" or "threshold coupled" chaotic maps. Such systems have been proposed for use in nonlinear computing and have been applied to classification problems in bioinformatics. We describe some of the attractors for such systems and prove general results about their basins of attraction. In particular, we show that the basins of attraction have infinitely many path components. We show that these components always accumulate at the corners of the domain of the system. For all threshold parameters above a certain value, we show that they accumulate at a Cantor set in the interior of the domain. For certain ranges of the threshold, we prove that the system has many attractors.

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