Diffusive hysteresis at high and low driving frequencies

Analytical theory of hysteresis in ion channels: two-state model

Channel-forming proteins in a lipid bilayer of a biological membrane usually respond to variation of external voltage by changing their conformations. Periodic voltages with frequency comparable with the inverse relaxation time of the protein produce hysteresis in the occupancies of the protein conformations. If the channel conductance changes when the protein jumps between these conformations, hysteresis in occupancies is observed as hysteresis in ion current through the channel. We develop an analytical theory of this phenomenon assuming that the channel conformational dynamics can be described in terms of a two-state model. The theory describes transient behavior of the channel after the periodic voltage is switched on as well as the shape and area of the hysteretic loop as functions of the frequency and amplitude of the applied voltage. The area vanishes as the voltage period T tends to zero and infinity. Asymptotic behaviors of the loop area A in the high- and low-frequency regimes, respectively, are A approximately T and A approximately T(-1).

Quantifying stochastic resonance: theory versus experiment

We discuss different quantifiers of stochastic resonance (SR) and how far they are mathematically related with each other. Specifically, we address bona fide SR in terms of the areas of the hysteresis loops and of the first peaks in the residence time distributions. We demonstrate a surprisingly good agreement of these two SR quantifiers experimentally for colloidal particles in periodically modulated laser traps. A simple theoretical model is established, which reproduces the experimental observations very well.

Suppression of noise in nonlinear systems subjected to strong periodic driving

An overdamped Brownian motion in "quartic" potential subjected to periodic driving has been considered. This system for the case of a weak periodic driving has been intensively studied during past decade within the context of stochastic resonance. It has been demonstrated that for the case of predominantly suprathreshold driving (the driving amplitude is significantly larger than the static threshold) the noise in the output signal is strongly suppressed at a certain frequency range: the signal-to-noise ratio demonstrates resonant behavior as a function of frequency.