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 L2 -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.
Galán
Roberto F
RF
Department of Neurosciences, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106, USA. rfgalan@case.edu
D000200:Action Potentials / Q000502:physiology*; D001683:Biological Clocks / Q000502:physiology*; D001698:Biomedical Engineering / Q000379:methods; D003198:Computer Simulation; D008959:Models, Neurological; D015233:Models, Statistical; D009415:Nerve Net / Q000502:physiology*; D009488:Neurosciences / Q000379:methods; D009991:Oscillometry / Q000379:methods*