Dynamical properties of strongly interacting Markov chains.
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.
Ay
Nihat
N
Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22-26, 04103 Leipzig, Germany. nay@mis.mpg.de
Wennekers
Thomas
T
D003198:Computer Simulation; D006801:Humans; D008390:Markov Chains; D008954:Models, Biological; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics; D013269:Stochastic Processes