Dynamical properties of strongly interacting Markov chains

Nihat Ay and Thomas Wennekers

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Submission date: 07. Jan. 2002
Pages: 32
published in: Neural networks, 16 (2003) 10, p. 1483-1497 
DOI number (of the published article): 10.1016/S0893-6080(03)00190-4
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Abstract:
Spatial interdependencies of stochastic units are usually 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 interdependencies, 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.