Synchronization in small-world systems

Details Synchronization in small-world systems Synchronization in small-world systems

2001-12-17

arxiv.org/abs/nlin/0112023v1

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1103/PhysRevLett.89.054101

We quantify the dynamical implications of the small-world phenomenon. We consider the generic synchronization of oscillator networks of arbitrary topology, and link the linear stability of the synchronous state to an algebraic condition of the Laplacian of the graph. We show numerically that the addition of random shortcuts produces improved network synchronizability. Further, we use a perturbation analysis to place the synchronization threshold in relation to the boundaries of the small-world region. Our results also show that small-worlds synchronize as efficiently as random graphs and hypercubes, and more so than standard constructive graphs.

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