Globally Coupled Maps: Almost Analytical Treatment of Phase Transitions

Details Globally Coupled Maps: Almost Analytical Treatment of Phase Transitions Globally Coupled Maps: Almost Analytical Treatment of Phase Transitions

1994-05-15

arxiv.org/abs/chao-dyn/9405008v1

Nonlinear Sciences

Chaotic Dynamics

26 pages, .dvi and postscript

Scientific paper

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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