Maximum entropy and stability of a random process with a power spectrum under deterministic action

The principle of maximum entropy has been used to analyze the stability of the resulting process observed during the interaction of a random process with a 1 / f spectrum and a deterministic action in lumped and distributed systems of nonlinear stochastic differential equations describing the coupled nonequilibrium phase transitions. Under the action of a harmonic force the stable resulting process is divided into two branches depending on the amplitude of the harmonic force. Under the action of exponential relaxation in a lumped system with an increase in the dumping coefficient the power spectrum of the resulting process becomes a spectrum of the Lorentz type.