Kinetic Ising System in an Oscillating External Field: Stochastic Resonance and Residence-Time Distributions

Experimental, analytical, and numerical results suggest that the mechanism by which a uniaxial single-domain ferromagnet switches after sudden field reversal depends on the field magnitude and the system size. Here we report new results on how these distinct decay mechanisms influence hysteresis in a two-dimensional nearest-neighbor kinetic Ising model. We present theoretical predictions supported by numerical simulations for the frequency dependence of the probability distributions for the hysteresis-loop area and the period-averaged magnetization, and for the residence-time distributions. The latter suggest evidence of stochastic resonance for small systems in moderately weak oscillating fields.Comment: Includes updated results for Fig.2 and minor text revisions to the abstract and text for clarit

Relation between Stochastic Resonance and Synchronization of Passages in a Double-Well System

We calculate, numerically, the residence times (and their distribution) of a Brownian particle in a two-well system under the action of a periodic, saw-tooth type, external field. We define hysteresis in the system. The hysteresis loop area is shown to be a good measure of synchronization of passages from one well to the other. We establish connection between this stochastic synchronization and stochastic resonance in the system.Comment: To appear in PRE May 1997, figures available on reques

Stochastic Resonance in Two Dimensional Landau Ginzburg Equation

We study the mechanism of stochastic resonance in a two dimensional Landau Ginzburg equation perturbed by a white noise. We shortly review how to renormalize the equation in order to avoid ultraviolet divergences. Next we show that the renormalization amplifies the effect of the small periodic perturbation in the system. We finally argue that stochastic resonance can be used to highlight the effect of renormalization in spatially extended system with a bistable equilibria

Coherent Signal Amplification in Bistable Nanomechanical Oscillators by Stochastic Resonance

Stochastic resonance is a counter-intuitive concept[1,2], ; the addition of noise to a noisy system induces coherent amplification of its response. First suggested as a mechanism for the cyclic recurrence of ice ages, stochastic resonance has been seen in a wide variety of macroscopic physical systems: bistable ring lasers[3], SQUIDs[4,5], magnetoelastic ribbons[6], and neurophysiological systems such as the receptors in crickets[7] and crayfish[8]. Although it is fundamentally important as a mechanism of coherent signal amplification, stochastic resonance is yet to be observed in nanoscale systems. Here we report the observation of stochastic resonance in bistable nanomechanical silicon oscillators, which can play an important role in the realization of controllable high-speed nanomechanical memory cells. Our nanomechanical systems were excited into a dynamic bistable state and modulated in order to induce controllable switching; the addition of white noise showed a marked amplification of the signal strength. Stochastic resonance in nanomechanical systems paves the way for exploring macroscopic quantum coherence and tunneling, and controlling nanoscale quantum systems for their eventual use as robust quantum logic devices.Comment: 18 pages, 4 figure

Long-lived states of oscillator chain with dynamical traps

A simple model of oscillator chain with dynamical traps and additive white noise is considered. Its dynamics was studied numerically. As demonstrated, when the trap effect is pronounced nonequilibrium phase transitions of a new type arise. Locally they manifest themselves via distortion of the particle arrangement symmetry. Depending on the system parameters the particle arrangement is characterized by the corresponding distributions taking either a bimodal form, or twoscale one, or unimodal onescale form which, however, deviates substantially from the Gaussian distribution. The individual particle velocities exhibit also a number of anomalies, in particular, their distribution can be extremely wide or take a quasi-cusp form. A large number of different cooperative structures and superstructures made of these formations are found in the visualized time patterns. Their evolution is, in some sense, independent of the individual particle dynamics, enabling us to regard them as dynamical phases.Comment: 8 pages, 5 figurs, TeX style of European Physical Journa

Multifractal characterization of stochastic resonance

We use a multifractal formalism to study the effect of stochastic resonance in a noisy bistable system driven by various input signals. To characterize the response of a stochastic bistable system we introduce a new measure based on the calculation of a singularity spectrum for a return time sequence. We use wavelet transform modulus maxima method for the singularity spectrum computations. It is shown that the degree of multifractality defined as a width of singularity spectrum can be successfully used as a measure of complexity both in the case of periodic and aperiodic (stochastic or chaotic) input signals. We show that in the case of periodic driving force singularity spectrum can change its structure qualitatively becoming monofractal in the regime of stochastic synchronization. This fact allows us to consider the degree of multifractality as a new measure of stochastic synchronization also. Moreover, our calculations have shown that the effect of stochastic resonance can be catched by this measure even from a very short return time sequence. We use also the proposed approach to characterize the noise-enhanced dynamics of a coupled stochastic neurons model.Comment: 10 pages, 21 EPS-figures, RevTe

Markov analysis of stochastic resonance in a periodically driven integrate-fire neuron

We model the dynamics of the leaky integrate-fire neuron under periodic stimulation as a Markov process with respect to the stimulus phase. This avoids the unrealistic assumption of a stimulus reset after each spike made in earlier work and thus solves the long-standing reset problem. The neuron exhibits stochastic resonance, both with respect to input noise intensity and stimulus frequency. The latter resonance arises by matching the stimulus frequency to the refractory time of the neuron. The Markov approach can be generalized to other periodically driven stochastic processes containing a reset mechanism.Comment: 23 pages, 10 figure

Effect of channel block on the spiking activity of excitable membranes in a stochastic Hodgkin-Huxley model

The influence of intrinsic channel noise on the spontaneous spiking activity of poisoned excitable membrane patches is studied by use of a stochastic generalization of the Hodgkin-Huxley model. Internal noise stemming from the stochastic dynamics of individual ion channels is known to affect the collective properties of the whole ion channel cluster. For example, there exists an optimal size of the membrane patch for which the internal noise alone causes a regular spontaneous generation of action potentials. In addition to varying the size of ion channel clusters, living organisms may adapt the densities of ion channels in order to optimally regulate the spontaneous spiking activity. The influence of channel block on the excitability of a membrane patch of certain size is twofold: First, a variation of ion channel densities primarily yields a change of the conductance level. Second, a down-regulation of working ion channels always increases the channel noise. While the former effect dominates in the case of sodium channel block resulting in a reduced spiking activity, the latter enhances the generation of spontaneous action potentials in the case of a tailored potassium channel blocking. Moreover, by blocking some portion of either potassium or sodium ion channels, it is possible to either increase or to decrease the regularity of the spike train.Comment: 10 pages, 3 figures, published 200

Statistics of transition times, phase diffusion and synchronization in periodically driven bistable systems

The statistics of transitions between the metastable states of a periodically driven bistable Brownian oscillator are investigated on the basis of a two-state description by means of a master equation with time-dependent rates. The results are compared with extensive numerical simulations of the Langevin equation for a sinusoidal driving force. Very good agreement is achieved both for the counting statistics of the number of transitions and the residence time distribution of the process in either state. The counting statistics corroborate in a consistent way the interpretation of stochastic resonance as a synchronisation phenomenon for a properly defined generalized Rice phase.Comment: 15 pages, 9 figure

Symmetry broken motion of a periodically driven Brownian particle: nonadiabatic regime

We report a theoretical study of an overdamped Brownian particle dynamics in the presence of both a spatially modulated one-dimensional periodic potential and a periodic alternating force (AF). As the periodic potential has a low symmetry (a ratchet potential) the Brownian particle displays a broken symmetry motion with a nonzero time average velocity. By making use of the Green function method and a mapping to the theory of Brillouin bands the probability distribution of the particle coordinate is derived and the nonlinear dependence of the macroscopic velocity on the frequency and the amplitude of AF is found. In particular, our theory allows to go beyond the adiabatic limit and to explain the peculiar reversal of the velocity sign found previously in the numerical analysis.Comment: 4 pages, 2 figure