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We study the overdamped dynamics of a Brownian particle in the double-well potential under the influence of an external periodic (AC) force with zero mean. We obtain a dependence of the jump rate on the frequency of the external force. The dependence shows a maximum at a certain driving frequency. We explain the phenomenon as a switching between different time scales of the system: interwell relaxation time (the mean residence time) and the intrawell relaxation time. Dependence of the resonant peak on the system parameters, namely the amplitude of the driving force A and the noise strength (temperature) D has been explored. We observe that the effect is well pronounced when A/D > 1 and if A/D 1 the enhancement of the jump rate can be of the order of magnitude with respect to the Kramers rate., Published in J. Phys. A: Math. Gen. 37 (2004) 6043-6051; 6 figures

We consider a bistable piecewise potential subject to both a periodic signal and a random force. The output signal-to-noise ratio (SNR) is calculated for a small-amplitude periodic signal of arbitrary frequency and noise strength D. Our analysis not only recovers the well known non-monotonic dependence of SNR on D at fixed , but also predicts the non-monotonic dependence of SNR on at fixed D. The latter phenomenon does not appear in the commonly assumed adiabatic approximation which applies only at low frequencies.

The authors investigate the effects of the synaptic noise in neural networks at finite temperatures. The analytic results are obtained through the use of the path-integral formulation which facilitates performing the quenched average over the random patterns and random noises. We consider the noise effects in the diluted Hopfield model, the fully-connected Hopfield model and the dynamic model, laying emphasis on the interplay with the temperature. In the phase diagrams drawn as functions of the temperature, the storage, and the noise strength, interesting features including re-entrance, first-order transitions as well as second-order transitions are found.

To describe a decay on an unstable state, a new systematic procedure is proposed for solving the Fokker-Planck equation with a small noise strength. The approximation assumes the correct small-time evolution and the Gaussian fluctuations around the most probable path for larger times. The exact stationary distribution is reached. The method may be easily adapted for calculating the multi-time correlation functions.