Fluctuations and waves in a spatially distributed system with the 1/f spectrum

A spatially distributed system with the 1/ f spectrum of fluctuation power is modeled by two nonlinear stochastic equations. The numerical methods show the formation of 1/ f and 1/ k spectra of extreme fluctuations against the background of the formation and motion of waves under the effect of white noise. The distribution of extreme fluctuations corresponds to the maximum of entropy, which testifies to their stability. Under an external periodic perturbation in the system, it is possible to observe space−time stochastic resonance.