Fluctuations in the limit cycle state and the problem of phase chaos

Gaussian fluctuations and first order fluctuation corrections to the deterministic solution are investigated in the framework of the generalized Ginzgurg-Landau type equation of motion exhibiting a hard mode transition leading to a homogeneous limit cycle state. It is shown that the stationary distribution of the fluctuations around the limit cycle is not of the form of a Ginzburg-Landau functional. The nature of the further instability in the post bifurcational region, resulting in the phase chaos in the deterministic problem, is found to be qualitatively changed by the presence of noise.