Control Of Stochastic Resonance Research Articles

Multiplexing-based control of stochastic resonance.

We show that multiplexing (Here, the term "multiplexing" means a special network topology where a one-layer network is connected to another one-layer networks through coupling between replica nodes. In the present paper, this term does not refer to the signal processing issues and telecommunications.) allows us to control noise-induced dynamics of multilayer networks in the regime of stochastic resonance. We illustrate this effect on an example of two- and multi-layer networks of bistable overdamped oscillators. In particular, we demonstrate that multiplexing suppresses the effect of stochastic resonance if the periodic forcing is present in only one layer. In contrast, multiplexing allows us to enhance the stochastic resonance if the periodic forcing and noise are present in all the interacting layers. In such a case, the impact of multiplexing has a resonant character: the most pronounced effect of stochastic resonance is achieved for an appropriate intermediate value of coupling strength between the layers. Moreover, multiplexing-induced enhancement of the stochastic resonance can become more pronounced for the increasing number of coupled layers. To visualize the revealed phenomena, we use the evolution of the dependence of the signal-to-noise ratio on the noise intensity for varying strength of coupling between the layers.

Stochastic Resonance Control by Coupling Two Fractional Bistable Systems

In order to enhance or produce stochastic resonance (SR), to obtain the required output response with specific properties, two bistable systems based on fractional over-damped Langevin equation are coupled into one multi-steady-state system via nonlinear method, one fractional bistable system where inherent parameters can be controlled is fed into the other system, the kinetic characteristics of the new coupled system is found much richer than each single fractional system. Theoretical analysis and numerical simulation results show that the SR can be enhanced or produced by adjusting parameters as coupling coefficient, fractional system inherent parameters as well as the external periodical signal amplitude while another fractional system’s parameters fixed. The coupled system has high practical value, which provides a reliable theoretical basis for the control and its applications of artificially generated stochastic resonance.

Control of Stochastic Resonance in Overdamped Fractional Langevin Equation

A system based on the model of overdamped fractional Langevin equation is constructed, the relation between fractional order and stochastic resonance is studied, it is found that stochastic resonance phenomenon is not produced or not obvious with given certain weak periodic signal and noise intensity. Applying external periodic signal is proposed to produce or strengthen stochastic resonance. The numerical simulations show that the stochastic resonance phenomenon can be effectively controlled, by changing the external periodic signal’s frequency or amplitude. We find the non-monotonic behaviors between the driving parameters and signal-to-noise(SNR). Optimal stochastic resonance can be achieved by adjusting one of the parameters as frequency and amplitude.

The Control of Stochastic Resonance by Harmonic Signal

The symmetry in a double-well potential of bistable systems subject to the action of a harmonic signal is broken. By variation of the amplitude of a harmonic signal, the asymmetry of bistable systems can be effectively controlled, the transitions probability between the two potential wells is increased and has influence on the effect of stochastic resonance in bistable systems. Numerical simulations show that adjusting the amplitude of a harmonic signal can produce stochastic resonance or make stochastic resonance more intense in bistable systems. It is a new method for stochastic resonance control.

Stochastic resonance in coupled underdamped bistable systems

We study onset and control of stochastic resonance (SR) phenomenon in two driven bistable systems, mutually coupled and subjected to independent noises, taking into account the influence of both the inertia and the coupling. In the absence of coupling, we found two critical damping parameters: one for the onset of SR and another for which SR is optimum. We then show that in weakly coupled systems, emergence of SR is governed by chaos. A strong coupling between the two oscillators induces coherence in the system; however, the systems do not synchronize no matter what the coupling is. Moreover, a specific coupling parameter is found for which the SR of each subsystem is optimum. Finally, a scheme for controlling SR in such coupled systems is proposed by introducing a phase difference between the two coherent driving forces.

Time-delayed feedback control of stochastic resonance induced by a multiplicative signal in a bistable system driven by cross-correlated noises

A linear time-delayed feedback is introduced into the bistable system driven by cross-correlated noises to control the stochastic resonance (SR) induced by the multiplicative periodic signal. The expression for the signal-to-noise ratio (SNR) of the system is derived in the small delay approximation and the adiabatic limit. By numerical computations, the effects of the delay time and strength of its feedback on the SNR are analyzed. The results indicate that the SR phenomenon can be enhanced or suppressed by adjusting the delay time and feedback strength. The influence of the time-delayed feedback on the SR depends not only on the sign of feedback strength, but also on the initial condition of the system. Moreover, both the delay time and the feedback strength can induce the critical behavior on the SR under given conditions.

Control of stochastic resonance in bistable systems by using periodic signals

According to the characteristic structure of double wells in bistable systems, this paper analyses stochastic fluctuations in the single potential well and probability transitions between the two potential wells and proposes a method of controlling stochastic resonance by using a periodic signal. Results of theoretical analysis and numerical simulation show that the phenomenon of stochastic resonance happens when the time scales of the periodic signal and the noise-induced probability transitions between the two potential wells achieve stochastic synchronization. By adding a bistable system with a controllable periodic signal, fluctuations in the single potential well can be effectively controlled, thus affecting the probability transitions between the two potential wells. In this way, an effective control can be achieved which allows one to either enhance or realize stochastic resonance.

The feedback control of stochastic resonance in bistable system

A feedback method is proposed to control the stochastic resonance by feeding back the output of bistable system to the input to re-act on the system. In a typical bistable system， the signal-to-noise ratio and spectral power amplification are considered as observable variables to evaluate the stochastic resonance effect. The stochastic resonance phenomenon caused by the linear or nonlinear feedback functions are studied respectively. The theoretical analysis and numerical simulation show that the stochastic resonance is controllable， and this method is especially suitable to the system of which the parameters are fixed or difficult to vary.

The stochastic resonance control of coupled bistable systems

Two bistable systems can become multistable through nonlinear coupling. The coupled system is more valuable than the single bistable system in theoretical research and practical application. The response characteristics of the coupled system subjecting to noise and periodic signal have been analytically analyzed to show the effect of coupled coefficient and bistable system parameters on stochastic resonance. The results show that the stochastic resonance is produced by the effect of zonal double-well potential. The schematic diagram of feedback coupled control principle has also been constructed. The method gives a reliable theoretical basis for artificially producing stochastic resonance or strengthening the effect of resonance in bistable system to control the stochastic resonance, and also for its application. The results of numerical simulation agree with that of theoretical analysis.

Stochastic resonance control based on vibration resonance

The dynamic characteristics of the non-linear bistable system subject to the action of high and low frequency signals were analyzed. The analytic formulation of the relationship between the parameters of high frequency signals and the SNR, spectral power amplification (SPA) of the bistable system output was presented. The stochastic resonance control method based on vibration resonance was proposed. The theoretical analysis and numerical simulation showed that the SNR and SPA of output signal of the bistable system can be controlled effectively by adjusting the amplitude and frequency of the high frequency signal.

Frequency matching method for stochastic resonance control

A frequency matching method for stochastic resonance control is presented on the assumption that stochastic synchronization of stochastic resonance will be generated when the nonlinear bistable system is stimulated by noise and weak periodic signal. Theoretical analysis and numerical simulation show that stochastic resonance can be controlled. Not only the frequency range of stochastic resonance can be broadened, but also the intensity of stochastic resonance can be strengthened by controlling the frequency of the input signal and statistical characteristics of noise, resulting in more noise energy being converted into signal energy.

Noninvasive control of stochastic resonance.

External feedback can enhance (or depress) the response of a noisy bistable system to monochromatic signals, significantly magnifying its natural stochastic resonance. We compare and contrast a variety of such feedback strategies, using both numerical simulations and analog electronic experiments. These noninvasive control techniques are especially valuable for noisy bistable systems that are difficult or impossible to modify internally.