Subordination of fast-relaxing degrees of freedom to order parameters under Ginzburg-Landau regimes

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Abstract
The role of fluctuations is studied in the locally attractive and locally invariant center manifold for a system which is a truncation of Hopf's model for hydrodynamic turbulence. The anlaysis is carried out in a regime where the system sustains a hard-mode instability and the real part of the Floquet coefficients does not change sign. The Gaussian width of the time-independent factor of the probability density is shown to measure the subordination of the fast-relaxing degree of freedom. A physically meaningful equation is derived relating the Gaussian width, the intensity of the additive noise, and the external control parameter. The characteristic curves of the reduced Fokker-Planck equation are the limit cycles derived from bifurcation theory.

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