Do globally coupled maps really violate the law of large numbers?

Arkady S. Pikovsky and Jürgen Kurths
Phys. Rev. Lett. 72, 1644 – Published 14 March 1994
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Abstract

Coherent behavior in ensembles of globally coupled maps is investigated in the limit of infinite number of elements. A self-consistent approach based on a nonlinear Frobenius-Perron equation is proposed for such systems, and a possibility of quasiperiodic and chaotic behavior of the mean field is demonstrated. For the study of finite ensembles a noisy nonlinear Frobenius-Perron equation is derived. Previous observations of violations of the law of large numbers are explained.

  • Received 27 September 1993

DOI:https://doi.org/10.1103/PhysRevLett.72.1644

©1994 American Physical Society

Authors & Affiliations

Arkady S. Pikovsky and Jürgen Kurths

  • Max-Planck-Arbeitsgruppe ‘‘Nichtlineare Dynamick,’’ Universität Potsdam, Potsdam, Germany

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Issue

Vol. 72, Iss. 11 — 14 March 1994

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