Estimation of periodicity in synchronised systems

The problem of estimating periodic properties of periodically non-stationary stochastic processes is studied. A recently introduced measure,(1,2) the measure of periodicity (MP), of stochastic oscillations is discussed. The MP estimates the "periodicity level" of the oscillations, i.e. the ratio of the periodic to the non-periodic components of the stochastic processes. The introduced measure differs fundamentally from the traditional measure, SNR, because the MP lets us estimate the value of the oscillation period. The MP is particularly useful in systems that display stochastic synchronisation phenomenon where the ratio of the periods of the external force and the response of the studied system is m:n, where m and n are positive integer numbers. The MP is used to study synchronisation in two different systems, a bistable system and a neuronal model driven by noise and a sinusoidal signal. The dependence of MP on parameters is compared with the behaviour of the cross-correlation coefficient and the effective diffusion coefficient. The influence of asymmetry in the bistable system is also studied. In the autonomous neuronal model it is shown that the coherence resonance phenomenon is well described by the MP