Analytical calculation of the frequency shift in phase oscillators driven by colored noise: Implications for electrical engineering and neuroscience

We provide an analytical expression for the mean frequency shift in phase oscillators as a function of the standard deviation, sigma and the autocorrelation time, tau of small random perturbations. We show that the frequency shift is negative and proportional to sigma(2). Its absolute value increases monotonically with tau, approaching an asymptote determined by the L-2-norm of the phase-response curve. We validate our theoretical predictions with computer simulations and discuss their implications for the design of electronic oscillators and for the encoding of information in biological neural networks.