Statistics of fluctuations with a 1/f spectrum at phase transitions in a spatially distributed system

A study has been made on the statistics of fluctuations in a spatially distributed system, which describes the interaction of nonequilibrium phase transitions. It is shown that at a certain intensity of external white noise acting on phase transitions, the time and spatial spectra of fluctuations have power laws S(f)∼f−α and S(k)∼k−γ. The dependence of the exponents α and γ on the value of the diffusion coefficient determining the spatial interaction of fluctuations have been found. Extreme low-frequency fluctuations has been revealed and distribution functions of their duration P(τ)∼τ−β and size P(s)∼s−ν have been determined. It has been found that the exponent α of the frequency dependence of time spectra and the exponent β of the distribution function of the fluctuation duration are related by the relation α+β=2. The exponent of the spatial spectrum γ and the exponent of the size distribution function ν are related by a similar relation: γ+ν=2.