Georgia Institute of Technology College of Sciences

Many complex biological and physical networks are naturally subject to both random influences, i.e., extrinsic randomness, from their surrounding environment, and uncertainties, i.e., intrinsic noise, from their individuals. Among many interesting network dynamics, of particular importance is the synchronization property which is closely related to the network reliability especially in cellular bio-networks. It has been speculated that whereas extrinsic randomness may cause noise-induced synchronization, intrinsic noises can drive synchronized individuals apart. This talk presents an appropriate framework of (discrete-state and discrete time) Markov random networks to incorporate both extrinsic randomness and intrinsic noise into the rigorous study of such synchronization and desynchronization scenario.  By studying the asymptotics of the Markov perturbed stationary distributions, probabilistic characterizations of the alternating pattern between synchronization and desynchronization behaviors is given.  More precisely, it is shown that if a random network without intrinsic noise perturbation is synchronized, then after intrinsic noise perturbation high-probability synchronization and low-probability desynchronization can occur intermittently and alternatively in time, and moreover, both the probability of (de)synchronization and the proportion of time spent in (de)synchrony can be explicitly estimated.