The phenomenon of stochastic resonance is investigated in an asymmetric bistable system with coloured noises. The approximate Fokker Planck equation is derived based on the Novikov theorem and the Fox approach. By app...The phenomenon of stochastic resonance is investigated in an asymmetric bistable system with coloured noises. The approximate Fokker Planck equation is derived based on the Novikov theorem and the Fox approach. By applying the two-state theory, the expression of the signal-to-noise ratio is obtained in the adiabatic limit. The effects of the noise parameters on signal-to-ratio are discussed. It is found that the stochastic resonance phenomena appear in most cases and disappear in some special cases.展开更多
This paper investigates the stochastic resonance (SR) phenomenon in an asymmetric system with coupling between multiplicative and additive noise when the coupling between two noise terms is coloured. The approximate...This paper investigates the stochastic resonance (SR) phenomenon in an asymmetric system with coupling between multiplicative and additive noise when the coupling between two noise terms is coloured. The approximate expression of signal-to-noise ratio has been obtained by applying the two-state theory and SR exhibits in the bistable system. Moreover, the potential asymmetry r and cross-correlation strength λ can weaken the SR phenomenon, while the cross-correlation time r can strengthen the SR phenomenon.展开更多
By adding frequency modulated signals to the intensity equation of gain noise model of the single-mode laser driven by two coloured noises which are correlated, this paper uses the linear approximation method to calcu...By adding frequency modulated signals to the intensity equation of gain noise model of the single-mode laser driven by two coloured noises which are correlated, this paper uses the linear approximation method to calculate the power spectrum and signal-to-noise ratio (SNR) of the laser intensity. The results show that the SNR appears typical stochastic resonance with the variation of intensity of the pump noise and quantum noise. As the amplitude of a modulated signal has effects on the SNR, it shows suppression, monotone increasing, stochastic resonance, and multiple stochastic resonance with the variation of the frequency of a carrier signal and modulated signal.展开更多
Weak signal reception is a very important and challenging problem for communication systems especially in the presence of non-Gaussian noise,and in which case the performance of optimal linear correlated receiver degr...Weak signal reception is a very important and challenging problem for communication systems especially in the presence of non-Gaussian noise,and in which case the performance of optimal linear correlated receiver degrades dramatically.Aiming at this,a novel uncorrelated reception scheme based on adaptive bistable stochastic resonance(ABSR)for a weak signal in additive Laplacian noise is investigated.By analyzing the key issue that the quantitative cooperative resonance matching relationship between the characteristics of the noisy signal and the nonlinear bistable system,an analytical expression of the bistable system parameters is derived.On this basis,by means of bistable system parameters self-adaptive adjustment,the counterintuitive stochastic resonance(SR)phenomenon can be easily generated at which the random noise is changed into a benefit to assist signal transmission.Finally,it is demonstrated that approximately 8dB bit error ratio(BER)performance improvement for the ABSR-based uncorrelated receiver when compared with the traditional uncorrelated receiver at low signal to noise ratio(SNR)conditions varying from-30dB to-5dB.展开更多
This paper considers the stochastic resonance in a stochastic bistable system driven by a periodic square-wave signal and a static force as well as by additive white noise and dichotomous noise from the viewpoint of s...This paper considers the stochastic resonance in a stochastic bistable system driven by a periodic square-wave signal and a static force as well as by additive white noise and dichotomous noise from the viewpoint of signal-to-noise ratio. It finds that the signal-to-noise ratio appears as stochastic resonance behaviour when it is plotted as a function of the noise strength of the white noise and dichotomous noise, as a function of the system parameters, or 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 on the signal-to-noise ratio is investigated.展开更多
This paper investigates the stochastic resonance in a time-delayed bistable system subjected to multiplicative and additive white noise and asymmetric dichotomous noise. Under the adiabatic approximation condition, th...This paper investigates the stochastic resonance in a time-delayed bistable system subjected to multiplicative and additive white noise and asymmetric dichotomous noise. Under the adiabatic approximation condition, the expression of the signal-to-noise ratio (SNR) is obtained. It finds that the SNR is a non-monotonic function of the delayed times, of the amplitude of the driving square-wave signal, as well as of the asymmetry of the dichotomous noise. In addition, the SNR varies non-monotonously with the intensities of the multiplicative and additive noise as well as the system parameters. Moreover, the SNR depends non-monotonically on the correlate rate of the dichotomous noise.展开更多
The effect of signal modulating noise in bistable stochastic resonance systems was studied theoretically and experimentally. A mathematical analysis was made on the bistable stochastic resonance model with small syste...The effect of signal modulating noise in bistable stochastic resonance systems was studied theoretically and experimentally. A mathematical analysis was made on the bistable stochastic resonance model with small system parameters. An analogue circuit was designed to perform the effect. The effect of signal modulating noise was shown in the analog simulation experiment. The analog experiment was conducted for two sinusoidal signals with different frequencies. The results show that there are a sinusoidal component corresponding to the input sinusoidal signal and a noise component presented as a Wiener process corresponding to the input white noise in the system output. By properly selecting system parameters, the effect of signal modulating noise can be manifested in the system output.展开更多
This paper investigates the stochastic resonance in a monostable system driven by square-wave signal, asymmetric dichotomous noise as well as by multiplicative and additive white noise. By the use of the properties of...This paper investigates the stochastic resonance in a monostable system driven by square-wave signal, asymmetric dichotomous noise as well as by multiplicative and additive white noise. By the use of the properties of the dichotomous noise, it obtains the expressions of the signal-to-noise ratio under the adiabatic approximation condition. It finds that the signal-to-noise ratio is a non-monotonic function of the asymmetry of the dichotomous noise, and which varies non- monotonously with the intensity of the multiplicative and additive noise as well as the system parameters. Moreover, the signal-to-noise ratio depends on the correlation rate and intensity of the dichotomous noise.展开更多
Based on adiabatic approximation theory,in this paper we study the asymmetric stochastic resonance system with time-delayed feedback driven by non-Gaussian colored noise.The analytical expressions of the mean first-pa...Based on adiabatic approximation theory,in this paper we study the asymmetric stochastic resonance system with time-delayed feedback driven by non-Gaussian colored noise.The analytical expressions of the mean first-passage time(MFPT)and output signal-to-noise ratio(SNR)are derived by using a path integral approach,unified colored-noise approximation(UCNA),and small delay approximation.The effects of time-delayed feedback and non-Gaussian colored noise on the output SNR are analyzed.Moreover,three types of asymmetric potential function characteristics are thoroughly discussed.And they are well-depth asymmetry(DASR),well-width asymmetry(WASR),and synchronous action of welldepth and well-width asymmetry(DWASR),respectively.The conclusion of this paper is that the time-delayed feedback can suppress SR,however,the non-Gaussian noise deviation parameter has the opposite effect.Moreover,the correlation time plays a significant role in improving SNR,and the SNR of asymmetric stochastic resonance is higher than that of symmetric stochastic resonance.Our experiments demonstrate that the appropriate parameters can make the asymmetric stochastic resonance perform better to detect weak signals than the symmetric stochastic resonance,in which no matter whether these signals have low frequency or high frequency,accompanied by strong or weak noise.展开更多
The stochastic resonance phenomenon in a harmonic oscillator with fluctuating intrinsic frequency by asymmetric dichotomous noise is investigated in this paper. By using the random average method and Shapiro- Loginov ...The stochastic resonance phenomenon in a harmonic oscillator with fluctuating intrinsic frequency by asymmetric dichotomous noise is investigated in this paper. By using the random average method and Shapiro- Loginov formula, the exact solution of the average output amplitude gain (OAG) is obtained. Numerical results show that OAG depends non-monotonically on the noise characteristics: intensity, correlation time and asymmetry. The maximum OAG can be achieved by tuning the noise asymmetry and or the noise correlation time.展开更多
This paper investigates the parameter-induced stochastic resonance using experimental methods in an over-damped random linear system with asymmetric dichotomous noise. Non-monotonic dependence of signal-to-noise ratio...This paper investigates the parameter-induced stochastic resonance using experimental methods in an over-damped random linear system with asymmetric dichotomous noise. Non-monotonic dependence of signal-to-noise ratio on the system parameter is observed. Several potential applications of parameter-induced stochastic resonance are given in circuits.展开更多
Stochastic resonance(SR) enhances the nonlinear system behavior with the assistance of noise, including the sensitivity and selectivity of the response to the exterior stimulus. The energy-transfer mechanism makes t...Stochastic resonance(SR) enhances the nonlinear system behavior with the assistance of noise, including the sensitivity and selectivity of the response to the exterior stimulus. The energy-transfer mechanism makes the weak information revealed in the output spectrum, while the time-waveform is distorted. The distortion analysis was made both from the particle's dynan-fics and signal processing. The factors causing the deviation in the output are presented and the function of the recovery system is proposed. By the investigation of the particle's motion track in the bistable system and the suggested recovery system, the influences of noise and system parameters on the recovery course were discussed. Moreover, the pulse distortion appearing the recovery waveform caused by the particle's transitions at the bistable potential' inflexions was explained. Due to different characteristics, cascaded-bistable SR or mono-stable SR was introduced to process different types of signals. The final recovery signal is just the suggested recovery system's response to the SR output. Meanwhile, the recovery system is optional, as parameter-tuned or parameter-fixed. Since the method requires no average processing, it is applicable to a single sample with limited length. The numerical simulations reveal that the SR recovery method can recover the waveform containing weak information submerged ha noise effectively. The engineering application to the vibration analysis of metal cutting chose the combination of mono-stable SR and the parameter-fixed recovery system. Because the optimal SR state is not required strongly, the system parameters are tuned in a wider range than the traditional SR processing methods.展开更多
The delay Fokker-Planck equation is given for an asymmetry bistable system with correlated Gaussian white noises. The small delay approximation based on the probability density approach is used and the approximate sta...The delay Fokker-Planck equation is given for an asymmetry bistable system with correlated Gaussian white noises. The small delay approximation based on the probability density approach is used and the approximate stationary probability density function is obtained. The phenomenon of delay induced transitions is found. When a weak periodic signal is added, the phenomenon of stochastic resonance is investigated. Expression of the signal-to-noise ratio (SNR) is obtained by using the two-state theory. It is shown that the time delay can suppress or promote the stochastic resonance phenomenon.展开更多
In this paper, the effect of every parameter (including p, q, r, λ, τ) on the mean first-passage time (MFPT) is investigated in an asymmetric bistable system driven by colour-correlated noise. The expression of ...In this paper, the effect of every parameter (including p, q, r, λ, τ) on the mean first-passage time (MFPT) is investigated in an asymmetric bistable system driven by colour-correlated noise. The expression of MFPT has been obtained by applying the steepest-descent approximation. Numerical results show that (1) the intensity of multiplicative noise p and the intensity of additive noise q play different roles in the MFPT of the system, (2) suppression appears on the curve of the MFPT with small λ (e.g. λ 〈 0.5) but there is a peak on the curve of the MFPT when λ is big (e.g. λ 〉 0.5), and (3) with different values of r (e.g. r = 0.1, 0.5, 1.5), the effort of τ on the MFPT is diverse.展开更多
By the method of the stochastic energetics,we investigate the stochastic resonance (SR) phenomenon of anoverdamped Brown particle in an asymmetric bistable potential,driven by external periodical signal and multiplica...By the method of the stochastic energetics,we investigate the stochastic resonance (SR) phenomenon of anoverdamped Brown particle in an asymmetric bistable potential,driven by external periodical signal and multiplicativenoise.The expressions have been obtained for the quasi-steady-state probability distribution function.It is found thatthe input energy (IE) pumped into the system by the external driving shows an SR-like behavior as a function of thenoise strength,whereas the IE turns to be a monotonic function of the correlation time of the noise.The effect ofpotential asymmetry is also studied on SR and IE.展开更多
The transient properties of an optical bistable system driven by multiplicative and additive noises are investigated. The effects of multiplicative and additive noises intensities on the mean first-passage times (MF...The transient properties of an optical bistable system driven by multiplicative and additive noises are investigated. The effects of multiplicative and additive noises intensities on the mean first-passage times (MFPTs) in two opposite directions are discussed. The results show that the intensities of multiplicative and additive noises affect the MFPTs on two directions in the same way.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 10672074)
文摘The phenomenon of stochastic resonance is investigated in an asymmetric bistable system with coloured noises. The approximate Fokker Planck equation is derived based on the Novikov theorem and the Fox approach. By applying the two-state theory, the expression of the signal-to-noise ratio is obtained in the adiabatic limit. The effects of the noise parameters on signal-to-ratio are discussed. It is found that the stochastic resonance phenomena appear in most cases and disappear in some special cases.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10472091 and 10332030)the Natural Science Foundation of Shaanxi Province (Grant No 2003A03)
文摘This paper investigates the stochastic resonance (SR) phenomenon in an asymmetric system with coupling between multiplicative and additive noise when the coupling between two noise terms is coloured. The approximate expression of signal-to-noise ratio has been obtained by applying the two-state theory and SR exhibits in the bistable system. Moreover, the potential asymmetry r and cross-correlation strength λ can weaken the SR phenomenon, while the cross-correlation time r can strengthen the SR phenomenon.
基金supported by the Key Project Scientific Research Foundation from the Education Department of Hubei Province of China(Grant No D200725001)
文摘By adding frequency modulated signals to the intensity equation of gain noise model of the single-mode laser driven by two coloured noises which are correlated, this paper uses the linear approximation method to calculate the power spectrum and signal-to-noise ratio (SNR) of the laser intensity. The results show that the SNR appears typical stochastic resonance with the variation of intensity of the pump noise and quantum noise. As the amplitude of a modulated signal has effects on the SNR, it shows suppression, monotone increasing, stochastic resonance, and multiple stochastic resonance with the variation of the frequency of a carrier signal and modulated signal.
基金supported in part by the National Natural Science Foundation of China(62001356)in part by the National Natural Science Foundation for Distinguished Young Scholar(61825104)+1 种基金in part by the National Key Research and Development Program of China(2022YFC3301300)in part by the Innovative Research Groups of the National Natural Science Foundation of China(62121001)。
文摘Weak signal reception is a very important and challenging problem for communication systems especially in the presence of non-Gaussian noise,and in which case the performance of optimal linear correlated receiver degrades dramatically.Aiming at this,a novel uncorrelated reception scheme based on adaptive bistable stochastic resonance(ABSR)for a weak signal in additive Laplacian noise is investigated.By analyzing the key issue that the quantitative cooperative resonance matching relationship between the characteristics of the noisy signal and the nonlinear bistable system,an analytical expression of the bistable system parameters is derived.On this basis,by means of bistable system parameters self-adaptive adjustment,the counterintuitive stochastic resonance(SR)phenomenon can be easily generated at which the random noise is changed into a benefit to assist signal transmission.Finally,it is demonstrated that approximately 8dB bit error ratio(BER)performance improvement for the ABSR-based uncorrelated receiver when compared with the traditional uncorrelated receiver at low signal to noise ratio(SNR)conditions varying from-30dB to-5dB.
基金Project supported by the Doctorial Foundation of Southwest University of Science and Technology of China(Grant No.08zx7108)
文摘This paper considers the stochastic resonance in a stochastic bistable system driven by a periodic square-wave signal and a static force as well as by additive white noise and dichotomous noise from the viewpoint of signal-to-noise ratio. It finds that the signal-to-noise ratio appears as stochastic resonance behaviour when it is plotted as a function of the noise strength of the white noise and dichotomous noise, as a function of the system parameters, or 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 on the signal-to-noise ratio is investigated.
基金supported by the Doctor Foundation of Southwest University of Science and Technology of China (Grant No. 08zx7108)
文摘This paper investigates the stochastic resonance in a time-delayed bistable system subjected to multiplicative and additive white noise and asymmetric dichotomous noise. Under the adiabatic approximation condition, the expression of the signal-to-noise ratio (SNR) is obtained. It finds that the SNR is a non-monotonic function of the delayed times, of the amplitude of the driving square-wave signal, as well as of the asymmetry of the dichotomous noise. In addition, the SNR varies non-monotonously with the intensities of the multiplicative and additive noise as well as the system parameters. Moreover, the SNR depends non-monotonically on the correlate rate of the dichotomous noise.
基金Project (10276032) supportedjointly by the National Natural Science Foundation of China and by the Science Foundationof China Academy of Engineering Physics NSAFproject(2005038228) supported by Postdoctoral Science Foundation of China projectsupported by the Postdoctoral Science Foundation of Central South University(2005)
文摘The effect of signal modulating noise in bistable stochastic resonance systems was studied theoretically and experimentally. A mathematical analysis was made on the bistable stochastic resonance model with small system parameters. An analogue circuit was designed to perform the effect. The effect of signal modulating noise was shown in the analog simulation experiment. The analog experiment was conducted for two sinusoidal signals with different frequencies. The results show that there are a sinusoidal component corresponding to the input sinusoidal signal and a noise component presented as a Wiener process corresponding to the input white noise in the system output. By properly selecting system parameters, the effect of signal modulating noise can be manifested in the system output.
基金Project supported by the Doctorial Foundation of Southwest University of Science and Technology of China(Grant No.08zx7108)
文摘This paper investigates the stochastic resonance in a monostable system driven by square-wave signal, asymmetric dichotomous noise as well as by multiplicative and additive white noise. By the use of the properties of the dichotomous noise, it obtains the expressions of the signal-to-noise ratio under the adiabatic approximation condition. It finds that the signal-to-noise ratio is a non-monotonic function of the asymmetry of the dichotomous noise, and which varies non- monotonously with the intensity of the multiplicative and additive noise as well as the system parameters. Moreover, the signal-to-noise ratio depends on the correlation rate and intensity of the dichotomous noise.
基金Project supported by the National Natural Science Foundation of China(Grant No.60551002)the Natural Science Foundation of Hunan Province,China(Grant No.2018JJ3680).
文摘Based on adiabatic approximation theory,in this paper we study the asymmetric stochastic resonance system with time-delayed feedback driven by non-Gaussian colored noise.The analytical expressions of the mean first-passage time(MFPT)and output signal-to-noise ratio(SNR)are derived by using a path integral approach,unified colored-noise approximation(UCNA),and small delay approximation.The effects of time-delayed feedback and non-Gaussian colored noise on the output SNR are analyzed.Moreover,three types of asymmetric potential function characteristics are thoroughly discussed.And they are well-depth asymmetry(DASR),well-width asymmetry(WASR),and synchronous action of welldepth and well-width asymmetry(DWASR),respectively.The conclusion of this paper is that the time-delayed feedback can suppress SR,however,the non-Gaussian noise deviation parameter has the opposite effect.Moreover,the correlation time plays a significant role in improving SNR,and the SNR of asymmetric stochastic resonance is higher than that of symmetric stochastic resonance.Our experiments demonstrate that the appropriate parameters can make the asymmetric stochastic resonance perform better to detect weak signals than the symmetric stochastic resonance,in which no matter whether these signals have low frequency or high frequency,accompanied by strong or weak noise.
文摘The stochastic resonance phenomenon in a harmonic oscillator with fluctuating intrinsic frequency by asymmetric dichotomous noise is investigated in this paper. By using the random average method and Shapiro- Loginov formula, the exact solution of the average output amplitude gain (OAG) is obtained. Numerical results show that OAG depends non-monotonically on the noise characteristics: intensity, correlation time and asymmetry. The maximum OAG can be achieved by tuning the noise asymmetry and or the noise correlation time.
文摘This paper investigates the parameter-induced stochastic resonance using experimental methods in an over-damped random linear system with asymmetric dichotomous noise. Non-monotonic dependence of signal-to-noise ratio on the system parameter is observed. Several potential applications of parameter-induced stochastic resonance are given in circuits.
基金supported by National Hi-tech Research and Development Program of China (863 Program, Grant No. 2007AA04Z414)National Natural Science Foundation of China (Grant No. 50675153)+1 种基金Tianjin Municipal Natural Science Foundation of China (Grant No. 07JCYBJC04600)Specialized Research Fund for Doctoral Program of Higher Education of China (Grant No. 20060056016)
文摘Stochastic resonance(SR) enhances the nonlinear system behavior with the assistance of noise, including the sensitivity and selectivity of the response to the exterior stimulus. The energy-transfer mechanism makes the weak information revealed in the output spectrum, while the time-waveform is distorted. The distortion analysis was made both from the particle's dynan-fics and signal processing. The factors causing the deviation in the output are presented and the function of the recovery system is proposed. By the investigation of the particle's motion track in the bistable system and the suggested recovery system, the influences of noise and system parameters on the recovery course were discussed. Moreover, the pulse distortion appearing the recovery waveform caused by the particle's transitions at the bistable potential' inflexions was explained. Due to different characteristics, cascaded-bistable SR or mono-stable SR was introduced to process different types of signals. The final recovery signal is just the suggested recovery system's response to the SR output. Meanwhile, the recovery system is optional, as parameter-tuned or parameter-fixed. Since the method requires no average processing, it is applicable to a single sample with limited length. The numerical simulations reveal that the SR recovery method can recover the waveform containing weak information submerged ha noise effectively. The engineering application to the vibration analysis of metal cutting chose the combination of mono-stable SR and the parameter-fixed recovery system. Because the optimal SR state is not required strongly, the system parameters are tuned in a wider range than the traditional SR processing methods.
基金supported by the National Natural Science Foundation of China (Grant No. 10872165, 10972181)Natural Science Foundation of Shaanxi Province, the Youth and Aoxiang Star Plan for Northwestern Polytechnical University Teachers’ Scientific and Technological Innovation Foundationthe Doctorate Creation Foundation of Northwestern Polytechnical University
文摘The delay Fokker-Planck equation is given for an asymmetry bistable system with correlated Gaussian white noises. The small delay approximation based on the probability density approach is used and the approximate stationary probability density function is obtained. The phenomenon of delay induced transitions is found. When a weak periodic signal is added, the phenomenon of stochastic resonance is investigated. Expression of the signal-to-noise ratio (SNR) is obtained by using the two-state theory. It is shown that the time delay can suppress or promote the stochastic resonance phenomenon.
基金Project supported by the National Natural Science Foundation of China (Grants Nos 10472091, 10332030 and 10502042) and the Graduate Starting Seed Fund of Northwestern Polytechnical University (Grant No Z200655).
文摘In this paper, the effect of every parameter (including p, q, r, λ, τ) on the mean first-passage time (MFPT) is investigated in an asymmetric bistable system driven by colour-correlated noise. The expression of MFPT has been obtained by applying the steepest-descent approximation. Numerical results show that (1) the intensity of multiplicative noise p and the intensity of additive noise q play different roles in the MFPT of the system, (2) suppression appears on the curve of the MFPT with small λ (e.g. λ 〈 0.5) but there is a peak on the curve of the MFPT when λ is big (e.g. λ 〉 0.5), and (3) with different values of r (e.g. r = 0.1, 0.5, 1.5), the effort of τ on the MFPT is diverse.
基金The project supported by Doctor Foundation of Panzhihua University under Grant No.B2006-1
文摘By the method of the stochastic energetics,we investigate the stochastic resonance (SR) phenomenon of anoverdamped Brown particle in an asymmetric bistable potential,driven by external periodical signal and multiplicativenoise.The expressions have been obtained for the quasi-steady-state probability distribution function.It is found thatthe input energy (IE) pumped into the system by the external driving shows an SR-like behavior as a function of thenoise strength,whereas the IE turns to be a monotonic function of the correlation time of the noise.The effect ofpotential asymmetry is also studied on SR and IE.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10472091 and 10332030, and the Natural Science Foundation of Shaanxi Province under Grant No 2003A03.
文摘The transient properties of an optical bistable system driven by multiplicative and additive noises are investigated. The effects of multiplicative and additive noises intensities on the mean first-passage times (MFPTs) in two opposite directions are discussed. The results show that the intensities of multiplicative and additive noises affect the MFPTs on two directions in the same way.