Large value fluctuations are modeled by a system of nonlinear stochastic equations describing the interacting phase transitions. Under the action of anisotropic white noise, random processes are formed with the 1/f^alpha dependence of the power spectra on frequency at values of the exponent from 0.7 to 1.7. It is shown that fluctuations with 1/f^alpha power spectra in the studied range of changes correspond to the entropy maximum, which indicates the stability of processes with 1/f^alpha power spectra at different values of the exponent alpha.
In the system of two nonlinear differential equations, proposed to explain the physical nature of the 1/f spectra, chaotization of the trajectories is revealed under periodic external action on one of the equations. External noise effects lead to stochastic resonance and low-frequency 1/f behavior of power spectra. Stochastic resonance and 1/f behavior of power spectra corresponds to the maximum information entropy, which indicates the stability of a random process.