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Synchronization stability in oscillator networks: Solution for asymmetrical configurations

Abstract We extend the connection graph stability method, originally developed for symmetrically coupled networks, to the general asymmetrical case. The principal new component of the method is the transformation of the directed connection graph into an undirected graph. The extension of the method to asymmetrical coupling consists in symmetrizing the graph and associating a weight to each path. This weight involves the node unbalance of the two nodes. The synchronization condition for this symmetrized-and-weighted network then also guarantees synchronization in the original non-symmetrical network.