Bifurcations in Globally Coupled Chaotic Maps

Abstract

We propose a new method to investigate collective behavior in a network of globally coupled chaotic elements generated by a tent map. In the limit of large system size, the dynamics is described with the nonlinear Frobenius-Perron equation. This equation can be transformed into a simple form by making use of the piecewise linear nature of the individual map. Our method is applied successfully to the analyses of stability of collective stationary states and their bifurcations.

12 pages, revtex, 10 figures

References in corpus (1)

• Bifurcations in Globally Coupled Map Lattices

Cited by in corpus (7)

• Collective Chaos
• On the Tongue-Like Bifurcation Structures of the Mean-Field Dynamics in a Network of Chaotic Elements
• Collective motion occurs inevitably in a class of populations of globally coupled chaotic elements
• On the Collective Motion in Globally Coupled Chaotic Systems
• Confined chaotic behavior in collective motion for populations of globally coupled chaotic elements
• Collective motions in globally coupled tent maps with stochastic updating
• Large deviations from the thermodynamic limit in globally coupled maps