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

A spatially distributed system with a 1/f power spectrum is described by two nonlinear stochastic equations. Conditions for the formation of auto-oscillations have been found using numerical methods. The formation of a 1/f and 1/k spectrum simultaneously with the formation and motion of waves under the action of white noise has been demonstrated. The large extreme fluctuations with 1/f and 1/k spectra correspond to the maximum entropy, which points to the stability of such processes. It is shown that on the background of formation and motion of waves at an external periodic action there appears spatio-temporal stochastic resonance, at which one can observe the expansion of the region of periodic pulsations under the action of white noise.