Bifurcations in Globally Coupled Map Lattices

Abstract

The dynamics of globally coupled map lattices can be described in terms of a nonlinear Frobenius--Perron equation in the limit of large system size. This approach allows for an analytical computation of stationary states and their stability. The complete bifurcation behaviour of coupled tent maps near the chaotic band merging point is presented. Furthermore the time independent states of coupled logistic equations are analyzed. The bifurcation diagram of the uncoupled map carries over to the map lattice. The analytical results are supplemented with numerical simulations.

19 pages, .dvi and postscript

References in corpus (1)

• Globally Coupled Maps: Almost Analytical Treatment of Phase Transitions

Cited by in corpus (10)

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• Bifurcations in Globally Coupled Chaotic Maps
• Periodicity Manifestations in the Turbulent Regime of Globally Coupled Map Lattice
• On the Collective Motion in Globally Coupled Chaotic Systems
• Collective motions in globally coupled tent maps with stochastic updating
• Large deviations from the thermodynamic limit in globally coupled maps
• Association schemes perspective of microbubble cluster in ultrasonic fields
• Periodicity Manifestations in the Non-Locally Coupled Maps
• Dynamics of inhomogeneous one--dimensional coupled map lattices