Resonant response of scale-invariant functions of a random process with a turbulent spectrum

Scale-invariant random processes with large fluctuations have been modeled by a system of two stochastic nonlinear differential equations describing interacting phase transitions. It is shown that under the action of white noise, a critical state arises, characterized by a turbulent spectrum and a scale-invariant distribution of amplitudes. The critical state corresponds to the maximum entropy, which indicates the stability of the process. An external harmonic action on a random process with a turbulent spectrum gives rise to a resonant response of scale-invariant functions.