scholarly journals Stochastic resonance in periodically driven bistable systems subjected to anomalous diffusion

2021 ◽  
Vol 3 (4) ◽  
Author(s):  
F. Naha Nzoupe ◽  
Alain M. Dikandé
Keyword(s):  
Stochastic Resonance ◽  
Signal To Noise Ratio ◽  
Planck Equation ◽  
Relevant Information ◽  
Periodic Signal ◽  
Signal To Noise ◽  
Periodically Driven ◽  
Loop Area ◽  
Bistable Systems ◽  
Noise Ratio

AbstractThe occurrence of stochastic resonance in bistable systems undergoing anomalous diffusions, which arise from density-dependent fluctuations, is investigated with an emphasis on the analytical formulation of the problem as well as a possible analytical derivation of key quantifiers of stochastic resonance. The nonlinear Fokker–Planck equation describing the system dynamics, together with the corresponding Ito–Langevin equation, is formulated. In the linear response regime, analytical expressions of the spectral amplification, of the signal-to-noise ratio and of the hysteresis loop area are derived as quantifiers of stochastic resonance. These quantifiers are found to be strongly dependent on the parameters controlling the type of diffusion; in particular, the peak characterizing the signal-to-noise ratio occurs only in close ranges of parameters. Results introduce the relevant information that, taking into consideration the interactions of anomalous diffusive systems with a periodic signal, can provide a better understanding of the physics of stochastic resonance in bistable systems driven by periodic forces.

STOCHASTIC RESONANCE IN BISTABLE AND EXCITABLE SYSTEMS: EFFECT OF NON-GAUSSIAN NOISES

2003 ◽  
Vol 03 (04) ◽  
pp. L365-L371 ◽  
Author(s):  
M. A. FUENTES ◽  
C. J. TESSONE ◽  
H. S. WIO ◽  
R. TORAL
Keyword(s):  
Stochastic Resonance ◽  
Gaussian Noise ◽  
Signal To Noise Ratio ◽  
Signal To Noise ◽  
Excitable System ◽  
Ratio Curve ◽  
Bistable Systems ◽  
Excitable Systems ◽  
Noise Ratio ◽  
Non Gaussian

We analyze stochastic resonance in systems driven by non-Gaussian noises. For the bistable double well we compare the signal-to-noise ratio resulting from numerical simulations with some quasi-analytical results predicted by a consistent Markovian approximation in the case of a colored non-Gaussian noise. We also study the FitzHugh–Nagumo excitable system in the presence of the same noise. In both systems, we find that, as the noise departs from Gaussian behavior, there is a regime (different for the excitable and the bistable systems) in which there is a notable robustness against noise tuning since the signal-to-noise ratio curve broadens and becomes less sensitive to the actual value of the noise intensity. We also compare our results with some experiments in sensory systems.

SIGNAL-TO-NOISE RATIO IN STOCHASTIC RESONANCE

1996 ◽  
Vol 10 (22) ◽  
pp. 1085-1094 ◽  
Author(s):  
A.K. CHATTAH ◽  
C.B. BRIOZZO ◽  
O. OSENDA ◽  
M.O. CÁCERES
Keyword(s):  
Stochastic Resonance ◽  
Brownian Particle ◽  
Theoretical Calculations ◽  
Signal To Noise Ratio ◽  
Planck Equation ◽  
Signal To Noise ◽  
Desktop Computer ◽  
Bistable Potential ◽  
Noise Ratio ◽  
Path Integral Method

We solve the Fokker-Planck equation for an overdamped Brownian particle in a periodically forced bistable potential by means of a path integral method, obtaining the propagators in the steepest-descent (small-noise) approximation. We compute the long-times asymptotic probability distribution, the asymptotic correlation functions, and the time-averaged spectral density, which allows us the immediate calculation of the signal to noise ratio, a directly measurable quantity useful to characterize the phenomenon of stochastic resonance. Our numerical algorithm is fast and runs on a desktop computer, and the results agree with experiments and with former theoretical calculations of the amplification factor; in addition it allows us to calculate the experimentally more accessible signal to noise ratio.

Stochastic Resonance in a Time-Delayed Logistic Growth Model Driven by Periodic Signal and White Noise

2011 ◽  
Vol 117-119 ◽  
pp. 703-707
Author(s):  
Yu Rong Zhou ◽  
Chong Qiu Fang
Keyword(s):  
White Noise ◽  
Stochastic Resonance ◽  
Growth Model ◽  
Delay Time ◽  
Signal To Noise Ratio ◽  
Logistic Growth ◽  
Periodic Signal ◽  
Signal To Noise ◽  
Logistic Growth Model ◽  
Noise Ratio

stochastic resonance; time-delayed Logistic growth model; signal-to-noise ratio Abstract. The stochastic resonance in a time-delayed Logistic growth model subject to correlated multiplicative and additive white noise as well as to multiplicative periodic signal is investigated. Using small time delay approximation, we get the expression of the signal-to-noise ratio (SNR). It is found that the SNR is a non-monotonic function of the system parameters, of the intensities of the multiplicative and additive noise, as well as of the correlation strength between the two noises. The effects of the delay time in the random force is in opposition to that of the delay time in the deterministic force.

NOISE IMPROVEMENTS IN STOCHASTIC RESONANCE: FROM SIGNAL AMPLIFICATION TO OPTIMAL DETECTION

2002 ◽  
Vol 02 (03) ◽  
pp. L221-L233 ◽  
Author(s):  
FRANÇOIS CHAPEAU-BLONDEAU ◽  
DAVID ROUSSEAU
Keyword(s):  
Stochastic Resonance ◽  
Signal Amplification ◽  
Signal To Noise Ratio ◽  
Periodic Signal ◽  
Optimal Detection ◽  
Input Output ◽  
Signal To Noise ◽  
Optimal Processing ◽  
Noise Ratio ◽  
Noise Benefits

It is demonstrated that benefits from the noise can be gained at various levels in stochastic resonance. Raising the noise can produce signal amplification as well as signal-to-noise ratio improvement, input–output gain exceeding unity in signal-to-noise ratio, and enhanced performance in optimal processing. This series of benefits is successively exhibited in the processing of a periodic signal coupled to a white noise through essentially static nonlinearities. Especially, it is established that noise benefits in stochastic resonance can extend up to optimal processing, by considering an optimal Bayesian detector whose performance is improvable by raising the level of the noise.

STOCHASTIC RESONANCE IN CHUA’S CIRCUIT DRIVEN BY AMPLITUDE OR FREQUENCY MODULATED SIGNALS

1994 ◽  
Vol 04 (02) ◽  
pp. 441-446 ◽  
Author(s):  
V.S. ANISHCHENKO ◽  
M.A. SAFONOVA ◽  
L.O. CHUA
Keyword(s):  
Numerical Simulation ◽  
Stochastic Resonance ◽  
Signal To Noise Ratio ◽  
Point Of View ◽  
Chua’S Circuit ◽  
Signal Distortion ◽  
Signal To Noise ◽  
Chua's Circuit ◽  
Noise Ratio ◽  
Modulated Signals

Using numerical simulation, we establish the possibility of realizing the stochastic resonance (SR) phenomenon in Chua’s circuit when it is excited by either an amplitude-modulated or a frequency-modulated signal. It is shown that the application of a frequency-modulated signal to a Chua’s circuit operating in a regime of dynamical intermittency is preferable over an amplitude-modulated signal from the point of view of minimizing the signal distortion and maximizing the signal-to-noise ratio (SNR).

SIGNAL-TO-NOISE RATIO GAIN IN NON-DYNAMICAL AND DYNAMICAL BISTABLE STOCHASTIC RESONATORS

2002 ◽  
Vol 02 (03) ◽  
pp. L147-L155 ◽  
Author(s):  
PETER MAKRA ◽  
ZOLTAN GINGL ◽  
LASZLO B. KISH
Keyword(s):  
Stochastic Resonance ◽  
Signal To Noise Ratio ◽  
Schmitt Trigger ◽  
Total Power ◽  
Signal To Noise ◽  
Simulation Techniques ◽  
Duty Cycles ◽  
Signal Simulation ◽  
Noise Ratio ◽  
Snr Gain

It has recently been reported that in some systems showing stochastic resonance, the signal-to-noise ratio (SNR) at the output can significantly exceed that at the input; in other words, SNR gain is possible. We took two such systems, the non-dynamical Schmitt trigger and the dynamical double wellpotential, and using numerical and mixed-signal simulation techniques, we examined what SNR gains these systems can provide. In the non-linear response limit, we obtained SNR gains much greater than unity for both systems. In addition to the classical narrow-band SNR definition, we also measured the ratio of the total power of the signal to the power of the noise part, and it showed even better signal improvement. Here we present a brief review of our results, and scrutinise, for both the Schmitt-trigger and the double well potential, the behaviour of the SNR gain by stochastic resonance for different signal amplitudes and duty cycles. We also discuss the mechanism of providing gains greater than unity.

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