Synchronization in Random Weighted Directed Networks
Porfiri, M.; Stilwell, D.J.; Bollt, E.M.
Circuits and Systems I: Regular Papers, IEEE Transactions on
Volume 55, Issue 10, Nov. 2008 Page(s):3170 - 3177
Digital Object Identifier   10.1109/TCSI.2008.925357
Summary:We assess synchronization of oscillators that are coupled via a time-varying stochastic network, modeled as a weighted directed random graph that switches at a given rate between a set of possible graphs. The existence of any graph edge is probabilistic and independent from the existence of any other edge. We further allow each edge to be weighted differently. Even if the network is always instantaneously not connected, we show that sufficient information is propagated through the network to allow almost sure local synchronization as long as the expected value of the network is connected, and that the switching rate is sufficiently fast.

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