Do globally coupled maps really violate the law of large numbers?
- 14 March 1994
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 72 (11) , 1644-1646
- https://doi.org/10.1103/physrevlett.72.1644
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.Keywords
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