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1.
HAN Yin-Xia LI Jing-Hui CHEN Shi-Gang 《理论物理通讯》2005,44(2):226-230
The phenomenon of stochastic resonance (SR) in a bistable nonlinear system is studied when the system is driven by the asymmetric potential and additive Gaussian colored noise. Using the unified colored noise approximation method, the additive Gaussian colored noise can be simplified to additive Gaussian white noise. The signal-to-noise ratio (SNR) is calculated according to the generalized two-state theory (shown in [H.S. Wio and S. Bouzat, Brazilian J.Phys. 29 (1999) 136]). We find that the SNR increases with the proximity of a to zero. In addition, the correlation time T between the additive Gaussian colored noise is also an ingredient to improve SR. The shorter the correlation time T between the Gaussian additive colored noise is, the higher of the peak value of SNR. 相似文献
2.
Effects of time delay on stochastic resonance of a periodically driven linear system with multiplicative and periodically modulated additive white noises
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Stochastic resonance (SR) of a periodically driven time-delayed
linear system with multiplicative white noise and periodically
modulated additive white noise is investigated. In the condition of
small delay time, an approximate analytical expression of output
signal-to-noise ratio (SNR) is obtained. The analytical results
indicate that (1) there exists a resonance peak in the curve for
SNR versus time delay; (2) the time delay will suspend the SR
dramatically for SNR versus other parameters of the system, such as
noise intensity, correlation intensity, and signal frequency, once a
certain value is reached, the SR phenomenon disappears. 相似文献
3.
Tao Yang Qinglin Han Chunhua Zeng Hua Wang Yunchang Fu Chun Zhang 《Central European Journal of Physics》2014,12(6):383-391
The phenomenon of stochastic resonance (SR) in a tumor growth model under the presence of immune surveillance is investigated. Time delay and cross-correlation between multiplicative and additive noises are considered in the system. The signal-to-noise ratio (SNR) is calculated when periodic signal is introduced multiplicatively. Our results show that: (i) the time delay can accelerate the transition from the state of stable tumor to that of extinction, however the correlation between two noises can accelerate the transition from the state of extinction to that of stable tumor; (ii) the time delay and correlation between two noises can lead to a transition between SR and double SR in the curve of SNR as a function of additive noise intensity, however for the curve of SNR as a function of multiplicative noise intensity, the time delay can cause the SR phenomenon to disappear, and the cross-correlation between two noises can lead to a transition from SR to stochastic reverse-resonance. Finally, we compare the SR phenomenon for the multiplicative periodic signal with that for additive periodic signal in the tumor growth model with immune surveillance. 相似文献
4.
PeiMing Shi HaiFeng Xia DongYing Han RongRong Fu 《Chinese Journal of Physics (Taipei)》2017,55(1):133-141
The dynamical complexity and stochastic resonance (SR) of a time-delayed asymmetric bistable system are studied. Firstly, The effective potential function and steady-state probability density function are deduced based on Born-Oppenheimer approximation theory, and we find that the asymmetric item and time-delayed feedback item can both affect the curve of these two functions, especially the asymmetric item can induce phase displacement. Secondly, the mean first-passage time (MFPT) which plays an important role in research on particles escape rate is derived and we obtain an approximate asymmetric item r which can maintain a steady MFPT. Finally, the influences of different parameters on SR are researched by signal-to-noise ratio (SNR). The analytic expression of SNR is derived and three dimensional graphs and contour maps of SNR with different parameters are obtained. The results indicate that time delay τ and time delay strength e can enhance the SNR and the asymmetric item r has a non-monotone effect on SNR. Notably, adjusting time delay strength e is more sensitive than that of the time delay τ in controlling SR. 相似文献
5.
We study the effect of time delay in the FitzHugh-Nagumo neural model with correlations between multiplicative and additive noise terms. Based on the corresponding Fokker-Planck equation, the explicit expressions of the stationary probability distribution function (SPDF), the mean first passage time (MFPT) and the signal-to-noise ratio (SNR) are obtained, respectively. Research results show that: (i) the system undergoes a succession of two phase transitions (i.e., the reentrance phenomenon) as the noise correlation parameter is increased and a (single) phase transition as the time delay is increased. (ii) The MFPT as a function of the multiplicative noise intensity exhibits a maximum. This maximum for MFPT identifies the noise enhanced stability (NES) effect, the noise correlation parameter intensifies the NES effect while the time delay, and the additive noise intensity weakens it. (iii) The existence of a maximum in the SNR as a function of the multiplicative noise intensity is the identifying characteristic of the stochastic resonance (SR) phenomenon, the noise correlation parameter enhances the SR while the time delay, and the additive noise intensity weaken it. 相似文献
6.
Influences of noise correlation and time delay on stochastic resonance induced by multiplicative signal in a cancer growth system
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This paper investigates the stochastic resonance (SR)
phenomenon induced by the multiplicative periodic signal in a cancer
growth system with the cross-correlated noises and time delay. To
describe the periodic change of the birth rate due to the periodic
treatment, a multiplicative periodic signal is added to the system.
Under the condition of small delay time, the analytical expression
of the signal-to-noise ratio R_{\rm SNR} is derived in the
adiabatic limit. By numerical calculation, the effects of the
cross-correlation strength \lambda and the delay time \tau on
R_{\rm SNR} are respectively discussed. The existence of a peak in
the curves of R_{\rm SNR} as a function of the noise intensities
indicates the occurrence of the SR phenomenon. It is found that
\lambda and \tau play opposite role on the SR phenomenon, i.e.,
the SR is suppressed by increasing \lambda whereas it is enhanced
with the increase of \tau, which is different from the case where
the periodic signal is additive. 相似文献
7.
C. H. Zeng H. Wang 《The European Physical Journal B - Condensed Matter and Complex Systems》2012,85(4):127
In this paper, we study the stochastic resonance (SR) in a geometrically confined system, where the irregular boundaries yield
entropic barriers. When the boundaries are subjected to periodic modulation, the output signal-to-noise ratio (SNR) is calculated.
The effects of the noise strength, the strength of the transversal force, the frequency and strength of modulation of the
walls of the enclosure are discussed. Our results show that: (i) it is interesting to observe a resonance peak in the SNR
as a function of the frequency of modulation, and therefore to the appearance of the entropic bona fide SR phenomenon; and
(ii) the resonance peak is more pronounced with decreasing strength of the transversal force and increasing strength of modulation. 相似文献
8.
Stochastic resonance in a bistable system with coloured correlation between additive and multiplicative noise
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The phenomenon of stochastic resonance (SR) in a bistable nonlinear system with coupling between additive and multiplicative noises is investigated when the correlation between two noise terms is coloured. It is found that the signal-to-noise ratio (SNR) of the system is affected not only by the coupling strength λ between two noise terms, but also by the noise correlation time τ. The SNR is changed from a single peak, to two peaks with a dip, and then to a monotonically decreasing function with noise strength. The dependence of the SR on the initial conditions is entirely caused by the coupling strength λ between two noise terms. 相似文献
9.
The stochastic resonance (SR) in a stochastic stable system driven by a static force and a periodic square-wave signal as well as by additive white noise and dichotomous noise is considered from the point of view of the signal-to-noise ratio (SNR). It is found that the SNR exhibits SR behavior when it is plotted as a function of the noise strength of the white noise and dichotomous noise, as well as when plotted as a function of the static force. Moreover, the influence of the strength of the stochastic potential force and the correlation rate of the dichotomous noise is investigated. 相似文献
10.
11.
Stochastic resonance (SR) in an over-damped linear system subjected to an excitation of bias signal modulated noise with multiplicative and additive noises is investigated. We obtain the exact expressions of the first two moments and the signal-to-noise ratio (SNR) of the output by using linear-response theory. The SNR depends non-monotonically on the intensity and the correlation time of multiplicative noise, the correlation time of additive noise, the intensity of the cross noise between multiplicative and additive noise, as well as the external field frequency. The conventional SR, the SR in a broad sense and the bona fide SR are found in the system. The influences of the asymmetries of multiplicative and additive noise, the correlation rate of the cross noise, the intensity of additive noise, the amplitude of signal and the bias on the SNR are analyzed. Moreover, we pointed out that SR can be realized by tuning the system parameter with fixed noise, i.e., parameter-induced stochastic resonance (PSR) exists. 相似文献
12.
Stochastic resonance in a gain--noise model of a single-mode laser driven by pump noise and quantum noise with cross-correlation between real and imaginary parts under direct signal modulation
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Stochastic resonance (SR) is studied in a gain--noise model of a
single-mode laser driven by a coloured pump noise and a quantum noise
with cross-correlation between real and imaginary parts under a
direct signal modulation. By using a linear approximation method, we
find that the SR appears during the variation of signal-to-noise
ratio (SNR) separately with the pump noise self-correlation time
\tau , the noise correlation coefficient between the real part and
the imaginary part of the quantum noise \lambdaq , the
attenuation coefficient \gamma and the deterministic steady-state
intensity I_0 . In addition, it is found that the SR can be
characterized not only by the dependence of SNR on the noise
variables of \tau and \lambdaq, but also by the
dependence of SNR on the laser system variables of \gamma and I0. Thus our investigation extends the characteristic quantity of SR
proposed before. 相似文献
13.
Kang-Kang Wang Wen-Wu Yu Qing-Yun Wang Sheng-Hong Li 《Chinese Journal of Physics (Taipei)》2018,56(1):158-170
In this paper, our aim is to investigate the steady state properties and stochastic resonance (SR) phenomenon for an ecological vegetation growth system with time delay induced by the multiplicative and additive noises. Numerical results show that the SR phenomenon caused by time delay, different noise terms and a weak periodic signal occurs in the vegetation growth model under different values of system parameters. With regard to the stationary state properties of the vegetation system, the results indicate that the terms of different noises and time delay can all accelerate the shift from the substantial state to the barren one of the ecological system, restrain the development of the vegetation system and weaken the stability of the ecological system. On the other hand, the additive noise strength always enhances the SNR and the SR phenomenon, while the intensity of multiplicative noise often reduces the effect of the SR. In particular, time delay can play different roles in exciting the SR phenomenon in different cases. 相似文献
14.
A. Igarashi L. Gulyás A. Ohsaki 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2012,66(3):1-6
The phenomenon of stochastic resonance (SR) driven by time-delayed feedback in a bistable system with colored noise is investigated. Combining the small time delay and unified colored noise approximation, the Fokker-Planck equation is obtained. The different effects of time delay and noise correlation time on stationary probability density and signal-to-noise ratio (SNR) are discussed respectively. It is found that time delay can markedly improve the output SNR. This method can be practically applied to many fields such as weak signal extraction, recovery and so on. Numerical simulations are presented and are in agreement with the approximate theoretical results. 相似文献
15.
16.
The stochastic resonance (SR) is studied in an overdamped linear system driven by multiplicative and additive noise when the additive noise is a linear combination of an asymmetric dichotomous noise and its square. The exact expressions are obtained for the first two moments and the correlation function and the SR phenomenon appeared. There are three different forms of SR: the bona fide SR, the conventional SR and SR in the broad sense. Moreover, the asymmetry of multiplicative noise has different effect on signal-to-ratio (SNR) for the first two different forms of SR and the effects of multiplicative noise and additive noise on SNR are different. 相似文献
17.
Effect of inertia mass on the stochastic resonance driven by a multiplicative dichotomous noise
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A stochastic system driven by dichotomous noise and periodic signal is investigated in the under-damped case.The exact expressions of output signal amplitude and signal-to-noise ratio(SNR) of the system are derived.Numerical results indicate that the inertial mass greatly affects the output signal amplitude and the SNR.Regardless of whether the noise is symmetric or asymmetric,the inertial mass can influence the phenomenon of stochastic resonance(SR) of the system,leading to two types of resonance phenomenon:one is coherence-resonance-like of the SNR with inertial mass,the other is the SR of the SNR with noise intensity. 相似文献
18.
X. Gu S. Zhu D. Wu 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2007,42(3):461-466
The steady state properties of a noise-driven bistable system are
investigated when there are two different kinds of time delays
existed in the deterministic and fluctuating forces respectively.
Using the approximation of the probability density approach, the
delayed Fokker-Planck equation is obtained. The stationary
probability distribution (SPD) and the variance of the system are
derived. It is found that the time delay τ in the deterministic
force can reduce the fluctuations while the time delay β in
the fluctuating force can enhance the fluctuations. Numerical
simulations are presented and are in good agreement with the
approximate theoretical results. 相似文献
19.
The effects of time delay on stochastic resonance (SR) in a bistable system with time delay, correlated noises and periodic
signal are studied by using the theory of signal-to-noise ratio (SNR). The expression of the SNR is derived under the adiabatic
limit and the small delay time approximation. It is found that: (i) For the case of no correlations between multiplicative
and additive noise, the delay time τ can enhance the SNR as a function of the multiplicative noise intensity α and it can restrain the SNR as a function of the additive noise intensity D; (ii) For the case of correlations between multiplicative and additive noise, τ can induce a minimum and maximum in curve of the SNR as a function of α, and can intensively restrain the SNR as a function of the D and there is a critical value of delay tim τ
c
=0.1 in the height of the SNR peak with change of τ, i.e., when τ takes value blow τ
c
, the τ boosts up the SNR as a function of the strength λ of correlations between multiplicative and additive noise, however, when τ takes value above τ
c
, the τ restrains that. 相似文献