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We study linear responses of a stochastic bistable system driven by dichotomic noise to a weak periodic signal. We show that the effect of stochastic resonance can be greatly enhanced in comparison with the conventional case when dichotomic forcing is absent, that is, both the signal-to-noise ratio and the spectral power amplification reach much greater values than in the standard stochastic resonance setup.

The subject of our study is a two-state dynamics driven by Gaussian white noise and a weak harmonic signal. The system resulting from a piecewise linear FizHugh-Nagumo model in the case of perfect time scale separation between fast and slow variables shows either bistable, excitable, or oscillatory behavior. Its output spectra as well as the spectral power amplification of the signal can be calculated for arbitrary noise strength and frequency, allowing characterization of the coherence resonance in the bistable and excitable regimes as well as quantification of nonadiabatic resonances with respect to the external signal in all regimes.

The phenomenon of noise-induced transport in ratchet devices offers an explanation for directed motion on the molecular scale observed in many biological systems. Net transport through a series of discrete states, occurring in cyclic processes or reactions, can be related to widely investigated continuous ratchet models in the context of thermally activated transitions. The transport process can be described effectively in terms of two characteristic coefficients: velocity and diffusion. Their relation to model parameters and limitations for the ratchet mechanism are discussed in this paper. As an application we consider a four-state model for uphill transmembrane transport and compare theoretical results with existing data from a related experiment.

We study, in terms of synchronization, the nonlinear response of noisy bistable systems to a stochastic external signal, represented by Markovian dichotomic noise. We propose a general kinetic model which allows us to conduct a full analytical study of the nonlinear response, including the calculation of cross-correlation measures, the mean switching frequency, and synchronization regions. Theoretical results are compared with numerical simulations of a noisy overdamped bistable oscillator. We show that dichotomic noise can instantaneously synchronize the switching process of the system. We also show that synchronization is most pronounced at an optimal noise level-this effect connects this phenomenon with aperiodic stochastic resonance. Similar synchronization effects are observed for a stochastic neuron model stimulated by a stochastic spike train.