Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2011-09-04
Physics
Condensed Matter
Statistical Mechanics
Submitted to Physica D, 6 Figures, main body 21 pages with 6 Appendices for technical aspects
Scientific paper
We consider the effect of correlated noise on the stability of synchronisation of oscillators on a general network. By examining the Kuramoto model in the neighborhood of a global phase synchronised fixed point the impact of the noise is seen in the time-dependent probability density. If the support of the distribution evolves outside the basin of attraction of a fixed point with finite probability the system is deemed to be unstable. By exactly solving the Fokker-Planck equation we find that quite different instabilities follow. For uncorrelated noise the instability is exponentially suppressed: for small diffusion constant, there is a vanishingly small probability that the system can drift out of phase synchronicity. With correlated noise applied to oscillator frequencies and the network coupling, the peak of the probability distribution itself drifts outside the basin of the fixed point and suppression becomes power-law. Correlated noise can therefore strongly de-stabilise phase synchronicity. The significance of result for general networks is discussed.
Kalloniatis Alexander C.
Zuparic Mathew
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