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Riddled Basins and Coupled Dynamical Systems

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Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems

Part of the book series: Lecture Notes in Physics ((LNP,volume 671))

Abstract

The collective dynamics of groups of coupled dynamical systems is of great interest for understanding spontaneous pattern formation in biological and many other systems; see for example [58]. One can learn a lot about such systems by first studying idealized cases where the systems are perfectly identical; this approach has been very successful in understanding general properties of synchronization as well as particular applications; see for example [77]. In this chapter we consider how this can lead to the appearance of attractors with riddled basins. These basins appear because symmetries of dynamical systems force the presence of invariant submanifolds; the attractors within invariant manifolds may be only weakly attracting transverse to the invariant manifold and this leads to a basin structure that is, roughly speaking, full of holes.

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  1. Department of Mathematical Sciences, Laver Building, University of Exeter, Exeter EX4 4QE,, UK

    P Ashwin

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Ashwin, P. Riddled Basins and Coupled Dynamical Systems. In: Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems. Lecture Notes in Physics, vol 671. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11360810_8

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