Scaling and Singularities in the Entrainment of Globally Coupled Oscillators
1995; American Physical Society; Volume: 74; Issue: 21 Linguagem: Inglês
10.1103/physrevlett.74.4341
ISSN1092-0145
Autores Tópico(s)stochastic dynamics and bifurcation
ResumoThe onset of collective behavior among oscillators with random frequencies is studied for globally coupled phase dynamical models. A Fokker-Planck equation for the phase distribution describes the dynamics including diffusion due to the noise in the frequencies. We analyze instabilities of the phase-incoherent state using amplitude equations for the unstable modes. In terms of the diffusion coefficient $D$, the linear growth rate \ensuremath{\gamma}, and the mode number $l$, the nonlinearly saturated mode amplitude typically scales like $|{\ensuremath{\alpha}}_{\ensuremath{\infty}}|\ensuremath{\sim}\sqrt{\ensuremath{\gamma}(\ensuremath{\gamma}{+l}^{2}D)}$. The unusual $\ensuremath{\gamma}{+l}^{2}D$ factor arises from a singularity in the cubic term of the amplitude equation.
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