Onset of Synchronization in Complex Networks of Noisy Oscillators

Details Onset of Synchronization in Complex Networks of Noisy Oscillators Onset of Synchronization in Complex Networks of Noisy Oscillators

2011-12-23

arxiv.org/abs/1112.5503v1

Nonlinear Sciences

Chaotic Dynamics

18 pages, 8 figures, 1 table

Scientific paper

We investigate the synchronization of phase oscillators with diverse frequencies on random networks. Each of the oscillators is driven by Gaussian white noise and the diversity of the oscillators is due to a corresponding frequency distribution. The structure of the network is quantified by the given degree distribution of the nodes. We approximate the network by a cluster of nodes that are all-to-all coupled and whose edges are weighted. Within this model we are able to formulate the effective dynamics for a single oscillator and to derive the corresponding Fokker-Planck equation. The latter allows in a self-consistent way to calculate the critical coupling strength for the onset of synchronized oscillation in the network. It is given as a product of two factors, where the first one depends solely on the network topology, while the second factor is a function of the noise intensity and the diversity of the oscillators. Our result is applied to a dense small-world network model and corroborated by numerical simulations.

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