Low-frequency fluctuations in stochastic processes with a 1/f α spectrum

The results of numerical analysis of the Brownian movement of a particle in the force field of the potential corresponding to interacting subcritical and supercritical phase transitions are considered. If the white noise intensity corresponds to the critical intensity of the noise-induced transition, the system of stochastic differential equations describes random steady-state processes with fluctuation power spectra inversely proportional to frequency f, S(f) similar to 1/f (alpha), where exponent alpha varies in the interval 0.8 a parts per thousand currency sign alpha a parts per thousand currency sign 1.8. Exponent beta of distribution function P(tau) similar to tau(-beta) for the duration of low-frequency extremal fluctuations, which are analogous to avalanches considered in the models of self-organized criticality in many respects, varies between the same limits. It is shown that exponents alpha and beta are connected through the relation alpha + beta = 2.