Mean Square Error Synchronization in Networks with Ring Structure

Abstract

A class of stochastic networks with ring structure is considered in which the flow of information depends on a Markov chain. We find sufficient conditions such that the mean square differences between the even or odd or all units in the network will eventually tend to zero. Such probabilistic synchronization then leads to pattern formation in our networks. Although we have discussed only one or two colored patterns, it is hoped that our investigations will lead to more interesting patterns in stochastic networks in the future.