Noise-induced oscillations in non-equilibrium steady state systems

We consider the effect of stochastic sources on the self-organization process being initiated with creation of the limit cycle. The general expressions obtained are applied to the stochastic Lorenz system to show that offset from the equilibrium steady state can destroy the limit cycle at a certain relation between characteristic scales of temporal variation of principal variables. Noise-induced resonance related to the limit cycle is found analytically to appear in the non-equilibrium steady state system if the fastest variations display a principal variable, which is coupled with two different degrees of freedom or more.