Dynamical properties of strongly interacting Markov chains

Authors:
Nihat Ay;Thomas Wennekers
Affiliations:
Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22-26, 04103 Leipzig, Germany;Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22-26, 04103 Leipzig, Germany
Venue:
Neural Networks
Year:
2003

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Abstract

Spatial interdependences of multiple stochastic units can be suitably quantified by the Kullback-Leibler divergence of the joint probability distribution from the corresponding factorized distribution. In the present paper, a generalized measure for stochastic interaction, which also captures temporal interdependences, is analysed within the setting of Markov chains. The dynamical properties of systems with strongly interacting stochastic units are analytically studied and illustrated by computer simulations. In particular, the emergence of determinism in such systems is demonstrated.