Globally Coupled Maps: Almost Analytical Treatment of Phase Transitions

Wolfram Just

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Globally Coupled Maps: Almost Analytical Treatment of Phase Transitions

Wolfram Just

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Abstract

Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a synchronized state. For coupled non--hyperbolic maps analytical and numerical evidence is given that arbitrary small coupling changes the dynamical behaviour. The anomalous dependence of fluctuations on the system size is attributed to these bifurcations.

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Wolfram Just. 1994-05-15. Globally Coupled Maps: Almost Analytical Treatment of Phase Transitions. https://arxiv.org/abs/chao-dyn/9405008

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