Remarks on the mean field dynamics of networks of chaotic elements

Kunihiko Kaneko

doi:10.1016/0167-2789(95)00097-n

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Remarks on the mean field dynamics of networks of chaotic elements

Kunihiko Kaneko

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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.

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Kunihiko Kaneko. 1994-07-07. Remarks on the mean field dynamics of networks of chaotic elements. https://doi.org/10.1016/0167-2789(95)00097-n

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