Asymptotic description of transients and synchronized states of globally coupled oscillators

Details Asymptotic description of transients and synchronized states of globally coupled oscillators Asymptotic description of transients and synchronized states of globally coupled oscillators

1997-06-13

arxiv.org/abs/patt-sol/9706003v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

Revtex,12 pag.,9 fig.;submitted to Physica D

Scientific paper

10.1016/S0167-2789(97)00197-8

A two-time scale asymptotic method has been introduced to analyze the multimodal mean-field Kuramoto-Sakaguchi model of oscillator synchronization in the high-frequency limit. The method allows to uncouple the probability density in different components corresponding to the different peaks of the oscillator frequency distribution. Each component evolves toward a stationary state in a comoving frame and the overall order parameter can be reconstructed by combining them. Synchronized phases are a combination of traveling waves and incoherent solutions depending on parameter values. Our results agree very well with direct numerical simulations of the nonlinear Fokker-Planck equation for the probability density. Numerical results have been obtained by finite differences and a spectral method in the particular case of bimodal (symmetric and asymmetric) frequency distribution with or without external field. We also recover in a very easy and intuitive way the only other known analytical results: those corresponding to reflection-symmetric bimodal frequency distributions near bifurcation points.

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