Stochastic Synchronization with Time Delays in Complex Networks

 

GYORGY KORNISS

RENSSELAER POLYTECHNIC INSTITUTE

 

We study the effects of finite time delays in stochastic synchronization problems on an arbitrary network. In the case of uniform delays across the network, using the known exact threshold value from the theory of differential equations with delays, we obtain synchronizability threshold (critical delay where synchronization breaks down) for an arbitrary network and the asymptotic scaling properties of the these thresholds in ensembles of large random networks. Further, we also numerically investigate the effects of heterogeneous delays in complex networks.