Exact solvable models of nonlinear dynamic systems driven by coloured Ornstein–Uhlenbeck and Rayleigh noises

Exact solutions of the stationary Kolmogorov–Fokker–Planck equations corresponding to a certain class of nonlinear dynamical systems of first order driven parametrically (multiplicatively) by colored Markov Ornstein–Uhlenbeck and Rayleigh noise are obtained. The influence of asymmetric fluctuations on the form of the stationary distributions is discussed. Phase diagrams are constructed for some examples, and phase transitions induced by colored Rayleigh noise are noted.