Exactly solvable model of continuous stationary 1∕f noise

An exactly solvable model generating a continuous random process with a 1∕f power spectrum is presented. Examples of such processes include the angular (phase) speed of trajectories near stable equilibrium points in two-dimensional dynamical systems perturbed by colored Gaussian noise. An exact formula giving the correlation function of the 1∕f noise in terms of the correlation of the perturbing colored noises is derived, and used to show that the 1∕f spectrum is found in a wide variety of cases. The 1∕f noise is non-Gaussian, as demonstrated by calculating its one-time probability distribution function. Numerical simulations confirm and extend the theoretical results.