Synchronization in Networks of Nonlinear Dynamical Systems Coupled via a Directed Graph

We study synchronization in an array of coupled identical nonlinear dynamical systems where the coupling topology is expressed as a directed graph and give synchronization criteria related to properties of a generalized Laplacian matrix of the directed graph. In particular, we extend recent results by showing that the array synchronizes for sufficiently large cooperative coupling if the underlying graph contains a spanning directed tree. This is an intuitive yet nontrivial result that can be paraphrased as follows: if there exists a dynamical system which influence directly or indirectly all other systems, then synchronization is possible for strong enough coupling. The converse is also true in general.

By: Chai Wah Wu

Published in: Nonlinearity , volume 18, (no 3), pages 1057-64 in 2005

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