Experimental evidence, numerics, and theory of vibrational resonance in bistable systems

Transport by bi-harmonic drives: from harmonic to vibrational mixing

Transport in a one-dimensional symmetric device can be activated by the combination of thermal noise and a bi-harmonic drive. The results of extensive simulations allow us to distinguish between two apparently different bi-harmonic regimes: (i) harmonic mixing, where the two drive frequencies are commensurate but not too high; (ii) vibrational mixing, where one harmonic drive component possesses a high frequency but finite amplitude-to-frequency ratio. A comparison with the earlier theoretical predictions shows that at present the analytical understanding of nonlinear frequency mixing is still not satisfactory.

Temporal fluctuation of singular values caused by dynamical noise in chaos

We propose a method to evaluate the influence of dynamical noise on chaotic systems. For Chua's electronic circuit as a typical chaotic system, it is demonstrated that dynamical noise influences the temporal fluctuation of singular values obtained from singular value decomposition. This behavior, however, is independent of additional measurement noise. The appearance of this fluctuation is compared to Shannon entropy of coarse-grained trajectories in its dependence on the noise amplitude. Additionally, noise-induced stabilization is discussed from the change of a pattern of a flip-flop process.

Noise-assisted transport on symmetric periodic substrates

The rectification of a massive Brownian particle moving on a periodic substrate can be achieved in the absence of spatial asymmetry, by having recourse to (at least) two periodic, zero-mean input signals. We determine the relevant drift current under diverse operation conditions, namely, additive and multiplicative couplings, adiabatic and fast oscillating drives, and propagating substrate modulations. Distinct rectification mechanisms result from the interplay of noise and commensuration of the input frequencies, mediated through the nonlinearity of the substrate. These mechanisms are then extended to characterize soliton transport along a directed multistable chain. As the side-wise soliton diffusion is ultimately responsible for the transverse diffusion of such chains, our approach provides a full account of the Brownian motion of both pointlike and linear objects on a periodic substrate.

Experimental and theoretical study of the noise-induced gain degradation in vibrational resonance

We present the results of theoretical and experimental investigations of the effect of additive noise on vibrational resonance in a bistable system driven by two periodic forces with very different frequencies. The phenomenon shows up as a parametric amplification of the low-frequency signal depending on the amplitude of high-frequency modulation. A scaling law for noise-induced decreasing of the gain factor, found theoretically, is compared with the experimental results obtained in a bistable vertical cavity surface emitting laser.

Effects of additive noise on vibrational resonance in a bistable system

We study the overdamped motion of a particle in a bistable potential subject to the action of a bichromatic force and additive noise, within the context of the vibrational resonance phenomenon. Under appropriate conditions, we obtain analytical expressions for the relevant observables which quantifies this phenomenon. The theoretical results are compared with those obtained by the numerical solution of the stochastic differential equation which describes the dynamics of the system. The limits of validity of the theoretical approach are also discussed.