Remarks on the mean field dynamics of networks of chaotic elements
Abstract
Fluctuations of the mean field of a globally coupled dynamical systems are discussed. The origin of hidden coherence is related with the instability of the fixed point solution of the self-consistent Perron-Frobenius equation. Collective dynamics in globally coupled tent maps are re-examined, both with the help of direct simulation and the Perron-Frobenius equation. Collective chaos in a single band state, and bifurcation against initial conditions in a two-band state are clarified with the return maps of the mean-field, Lyapunov spectra, and also the newly introduced Lyapunov exponent for the Perron-Frobenius equation. Future problems on the collective dynamics are discussed.
Keywords
Cite
@article{arxiv.chao-dyn/9407002,
title = {Remarks on the mean field dynamics of networks of chaotic elements},
author = {Kunihiko Kaneko},
journal= {arXiv preprint arXiv:chao-dyn/9407002},
year = {2015}
}
Comments
15 pages; original has 15 figures which are not included here. Submitted to the special issue of Physica D as the proceedings for "Gran Finale"