Physics – Data Analysis – Statistics and Probability
Scientific paper
1999-06-23
Physics
Data Analysis, Statistics and Probability
54 pages, including 12 eps figures; uses elsart.cls
Scientific paper
10.1016/S0167-2789(00)00056-7
Systems of a large number N of globally coupled maps have become popular as a relatively simple prototype of high-dimensional dynamics, showing many interesting and typical phenomena like synchronisation, cluster formation and multistability, and having potential applications in systems like Josephson junction arrays or in biophysical models. There exists a wealth of numerical investigations of globally coupled maps. While much progress has been made in the explanation of the macroscopic behaviour of such systems in the limit of infinite N, there is still need for a sound theory about the asymptotic behaviour of finite-N systems as N approaches infinity. This article introduces a method by which it is possible to obtain asymptotic estimates for long-term deviations from the thermodynamic limit behaviour. This method is based upon the concept of quasipotentials, originally developed by Freidlin, Wentzell, and others for describing the influence of small random perturbations on the long-term behaviour of dynamical systems. The problems of explicitly computing quasipotentials in the present context and potential approximation schemes are discussed. All the concepts described in this article are illustrated with a simple example.
No associations
LandOfFree
Large deviations from the thermodynamic limit in globally coupled maps does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Large deviations from the thermodynamic limit in globally coupled maps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Large deviations from the thermodynamic limit in globally coupled maps will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-29020