Bifurcations in Globally Coupled Map Lattices
chao-dyn
2016-08-14 v1 Chaotic Dynamics
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.
Cite
@article{arxiv.chao-dyn/9405009,
title = {Bifurcations in Globally Coupled Map Lattices},
author = {Wolfram Just},
journal= {arXiv preprint arXiv:chao-dyn/9405009},
year = {2016}
}
Comments
19 pages, .dvi and postscript