Bifurcations in globally coupled map lattices

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Apr 1995Embargo end date: 01 May 1994 English Publisher:Springer Science and Business Media LLCJournal:Journal of Statistical Physics, volume 79, pages 429-449 (issn: 0022-4715, eissn: 1572-9613,

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Authors: Just, Wolfram;

doi: 10.1007/bf02179397 , 10.48550/arxiv.chao-dyn/9405009

arXiv: chao-dyn/9405009

Bifurcations in globally coupled map lattices

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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

Related Organizations

Darmstadt University of Applied Sciences
Germany

Keywords

nonhyperbolic effects, FOS: Physical sciences, coupled map lattice, Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics, Chaotic Dynamics (nlin.CD), Topological dynamics, stability analysis, Nonlinear Sciences - Chaotic Dynamics

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