1995/01/03 by John David Crawford · 1 citation
Physics and Astronomy · #adap-org #nlin.AO
paper · pdf · doi:10.1103/physrevlett.74.4341
published as Phys. Rev. Lett. 74, 4341 (1995) · 11 pages (Revtex); paper submitted to Phys. Rev. Lett
arxiv created 1995/01/03 · arxiv updated 2009/11/30
The onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling. The population is described by a Fokker-Planck equation for the distribution of phases which includes the diffusive effect of noise in the oscillator frequencies. The bifurcation from the phase-incoherent state is analyzed using amplitude equations for the unstable modes with particular attention to the dependence of the nonlinearly saturated mode |α_∞| on the linear growth rate γ. In general we find |α_∞|∼ √(γ(γ+l2D)) where D is the diffusion coefficient and l is the mode number of the unstable mode. The unusual (γ+l2D) factor arises from a singularity in the cubic term of the amplitude equation.