Stochastic resonance phenomenon in an underdamped bistable system driven by weak asymmetric dichotomous noise

2012 ◽  
Vol 70 (1) ◽  
pp. 531-539 ◽  
Author(s):  
Yong Xu ◽  
Juan Wu ◽  
Hui-Qing Zhang ◽  
Shao-Juan Ma
Keyword(s):  
Stochastic Resonance ◽  
Resonance Phenomenon ◽  
Bistable System ◽  
Dichotomous Noise ◽  
Asymmetric Dichotomous Noise ◽  
Stochastic Resonance Phenomenon

scholarly journals The Stochastic Resonance Phenomenon of Different Noises in Underdamped Bistable System

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Shan Yang ◽  
Zening Fan ◽  
Ruibin Ren
Keyword(s):  
Stochastic Resonance ◽  
Resonance Phenomenon ◽  
Bistable System ◽  
Resonance Problem ◽  
Control Effect ◽  
Bistable Systems ◽  
Spectrum Density ◽  
Factors Of Influence ◽  
Asymmetric Dichotomous Noise ◽  
Stochastic Resonance Phenomenon

In this paper, the stochastic resonance (SR) phenomenon of four kinds of noises (the white noise, the harmonic noise, the asymmetric dichotomous noise, and the Lévy noise) in underdamped bistable systems is studied. By applying theory of stochastic differential equations to the numerical simulation of stochastic resonance problem, we simulate and analyze the system responses and pay close attention to stochastic control in the proposed systems. Then, the factors of influence to the SR are investigated by the Euler-Maruyama algorithm, Milstein algorithm, and fourth-order Runge-Kutta algorithm, respectively. The results show that the SR phenomenon can be generated in the proposed system under certain conditions by adjusting the parameters of the control effect with different noises. We also found that the type of the noise has little effect on the resonance peak of the output power spectrum density, which is not observed in conventional harmonic systems driven by multiplicative noise with only an overdamped term. Therefore, the conclusion of this paper can provide experimental basis for the further study of stochastic resonance.

STOCHASTIC RESONANCE IN A BISTABLE SYSTEM DRIVEN BY WEAK PERIODIC SIGNAL WITH MULTIPLE DELAYS

2011 ◽  
Vol 25 (13) ◽  
pp. 1775-1783 ◽  
Author(s):  
HUI-QING ZHANG ◽  
WEI XU ◽  
CHUN-YAN SUN ◽  
YONG XU
Keyword(s):  
Probability Density ◽  
Stochastic Resonance ◽  
State Theory ◽  
Resonance Phenomenon ◽  
Bistable System ◽  
Periodic Signal ◽  
Multiple Delays ◽  
Small Delay ◽  
Stochastic Resonance Phenomenon ◽  
Good Agreement

The phenomenon of stochastic resonance in a bistable system with multiple delays is investigated. The analytic expression of approximation stationary probability density is obtained by using small delay approximation based on probability density approach. Numerical simulation is performed and it is shown that the analytic results are in good agreement with Monte Carlo simulation. Then the expression of the signal-to-noise (SNR) is derived by using two-state theory. Finally, the effect of multiple delays on SNR is discussed. It is found that the stochastic resonance phenomenon can be suppressed or promoted when multiple delays are increased.

STOCHASTIC RESONANCE OF A LINEAR SYSTEM INDUCED BY DICHOTOMOUS NOISE

2008 ◽  
Vol 22 (06) ◽  
pp. 697-708
Author(s):  
YU-RONG ZHOU ◽  
FENG GUO ◽  
SHI-QI JIANG ◽  
XIAO-FENG PANG
Keyword(s):  
Linear System ◽  
External Field ◽  
Stochastic Resonance ◽  
Linear Response ◽  
Signal To Noise Ratio ◽  
Linear Response Theory ◽  
Resonance Phenomenon ◽  
Field Frequency ◽  
Dichotomous Noise ◽  
Stochastic Resonance Phenomenon

The stochastic resonance phenomenon in a linear system subject to multiplicative and additive dichotomous noise is investigated. By the use of the linear-response theory and the properties of the dichotomous noise, the exact expressions have been found for the first two moments and the signal-to-noise ratio (SNR). It is shown that the SNR is a non-monotonic function of the correlation time of the additive dichotomous noise, and it varies non-monotonically with the bias of the external field, with the intensity and asymmetry of the multiplicative dichotomous noise, as well as with the external field frequency. Moreover, the SNR depends on the intensity of the cross noise between the multiplicative and additive dichotomous noise, as well as on the strength and asymmetry of the additive dichotomous noise.

Stochastic Resonance Enhanced by Colored Multiplicative and Additive Noises in a Time-Delayed Bistable System

2012 ◽  
Vol 538-541 ◽  
pp. 2598-2601
Author(s):  
Feng Bao Li ◽  
Xiao Yan Lei ◽  
Fu Cheng Zhu
Keyword(s):  
Stochastic Resonance ◽  
Colored Noise ◽  
Signal To Noise Ratio ◽  
Bistable System ◽  
Constant Force ◽  
Signal To Noise ◽  
Dichotomous Noise ◽  
Square Wave ◽  
Wave Signal ◽  
Asymmetric Dichotomous Noise

The phenomenon of stochastic resonance (SR) in a time-delayed bistable system with square-wave signal, a constant force, with asymmetric dichotomous noise and multiplicative and additive colored noise is investigated. It is found that, the SR behavior can be observed on the signal-to-noise ratio (SNR) curves as a function of the intensity and asymmetry of the dichotomous noise, as a function of the amplitude of the square-wave, the constant force, as well as of the strength of the colored noises.

On representing noise by deterministic excitations for interpreting the stochastic resonance phenomenon

2021 ◽  
Vol 379 (2192) ◽  
pp. 20200229 ◽  
Author(s):  
V. Sorokin ◽  
I. Demidov
Keyword(s):  
Stochastic Resonance ◽  
High Frequency ◽  
Stochastic Systems ◽  
Signal To Noise Ratio ◽  
Nonlinear Damping ◽  
Resonance Phenomenon ◽  
Oscillatory Systems ◽  
Stochastic Excitations ◽  
Viable Approach ◽  
Stochastic Resonance Phenomenon

Adding noise to a system can ‘improve’ its dynamic behaviour, for example, it can increase its response or signal-to-noise ratio. The corresponding phenomenon, called stochastic resonance, has found numerous applications in physics, neuroscience, biology, medicine and mechanics. Replacing stochastic excitations with high-frequency ones was shown to be a viable approach to analysing several linear and nonlinear dynamic systems. For these systems, the influence of the stochastic and high-frequency excitations appears to be qualitatively similar. The present paper concerns the discussion of the applicability of this ‘deterministic’ approach to stochastic systems. First, the conventional nonlinear bi-stable system is briefly revisited. Then dynamical systems with multiplicative noise are considered and the validity of replacing stochastic excitations with deterministic ones for such systems is discussed. Finally, we study oscillatory systems with nonlinear damping and analyse the effects of stochastic and deterministic excitations on such systems. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

Effect of White Noise and Dichotomous Noise in a Bistable System

2011 ◽  
Vol 295-297 ◽  
pp. 2143-2146 ◽  
Author(s):  
Feng Guo ◽  
Xiao Feng Cheng ◽  
Xiao Dong Yuan ◽  
Shao Bo He
Keyword(s):  
White Noise ◽  
Adiabatic Approximation ◽  
Additive Noise ◽  
Signal To Noise Ratio ◽  
Bistable System ◽  
Signal To Noise ◽  
Dichotomous Noise ◽  
System Parameters ◽  
Additive White Noise ◽  
Asymmetric Dichotomous Noise

The stochastic resonance in a bistable system subject to asymmetric dichotomous noise and multiplicative and additive white noise is investigated. By using the properties of the dichotomous noise, under the adiabatic approximation condition, the expression of the signal-to-noise ratio (SNR) is obtained. It is found that the SNR is a non-monotonic function of the asymmetry of the dichotomous noise, and it varies non-monotonously with the intensities of the multiplicative and additive noise as well as with the system parameters. Moreover, the SNR depends on the correlation rate of the dichotomous noise.

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