Bifurcations in Globally Coupled Map Lattices

Details Bifurcations in Globally Coupled Map Lattices Bifurcations in Globally Coupled Map Lattices

1994-05-15

arxiv.org/abs/chao-dyn/9405009v1

Nonlinear Sciences

Chaotic Dynamics

19 pages, .dvi and postscript

Scientific paper

10.1007/BF02179397

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.

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