THE SPECTRAL DENSITY OF NONLINEAR O-U NOISE AND THE INFLUENCE OF NONLINEAR FLUCTUATION ON THE TRANSITION OF BISTABLE SYSTEM

A stochastic differential equation driven by N-order nonlinear fluctua tion is investigated by defining a novel stochastic process Gamma(t). The spectral densities of Gamma(t) for N = 1, 2, 3 and 4 are obtained. We compare the results of the linear fluctuation case with the nonlin ear fluctuation case and find that the extremum of the spectral densit y for linear case is directly proportional to the noise intensity D an d independent of the correlation time tau, the extremum of the spectra l density for nonlinear case is determined by both D and tau. An appro ximate Fockker-Planck equation of the N-order nonlinear fluctuation is derived by Hanggi-like ansatz. The influences of nonlinear fluctuatio n on the transition of bistable system are studied. It is found that t he area of unimodal region and bimodal legion of the stationary probab ility is independent of D and tau for linear case, however, the area o f two regions is related to D and tau for nonlinear case.