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
Stochastic resonance（SR） is studied in an under-damped bistable system driven by the harmonic mixing signal and Gaussian white noise. Using the linear response theory（LRT）, the expressions of the spectral amplific...Stochastic resonance（SR） is studied in an under-damped bistable system driven by the harmonic mixing signal and Gaussian white noise. Using the linear response theory（LRT）, the expressions of the spectral amplification at fundamental and higher-order harmonic are obtained. The effects of damping coefficient, noise intensity, signal amplitude, and frequency on spectral amplifications are explored. Meanwhile, the power spectral density（PSD） and signal-to-noise ratio（SNR） are calculated to quantify SR and verify the theoretical results. The SNRs at the first and second harmonics exhibit a minimum first and a maximum later with increasing noise intensity. That is, both of the noise-induced suppression and resonance can be observed by choosing proper system parameters. Especially, when the ratio of the second harmonic amplitude to the fundamental one takes a large value, the SNR at the fundamental harmonic is a monotonic function of noise intensity and the SR phenomenon disappears.展开更多
The steady-state properties of a bistable system are investigated when both the multiplicative noise and the coupling between additive and multiplicative noises are coloured with different values of noise correlation ...The steady-state properties of a bistable system are investigated when both the multiplicative noise and the coupling between additive and multiplicative noises are coloured with different values of noise correlation times T1 and T2. After introducing a dimensionless parameter R（R = α/D, D is the intensity of the multiplicative noise and a is the intensity of the additive noise）, and performing the numerical computations, we find the following points： （1） For the case of R 〉 1, A （the intensity of correlation between additive and multiplicative noises）, T1 and T2 can induce the stationary probability distribution （SPD） transition from bimodal to unimodal in structure, but for the cases of R _〈 1, the bimodal structure is preserved; （2） a can also induce the SPD transition from bimodal to unimodal in structure; （3） the bimodal structure of the SPD exhibits a symmetrical structure as D increases.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
The asymmetric effects on the escape rates from the stable states x±in the bistable system are analyzed. The results indicate that the multiplicative noise and the additive noise always enhance the particle escap...The asymmetric effects on the escape rates from the stable states x±in the bistable system are analyzed. The results indicate that the multiplicative noise and the additive noise always enhance the particle escape from stable states x±of bistable.However,the asymmetric parameter r enhances the particle escape from stable state x_+,and holds back the particle escape from stable state x_-.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 multiplicati...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 mean first-passage time of a bistable system with time-delayed feedback driven by multiplicative non-Gaussian noise and additive Gaussian white noise is investigated. Firstly, the non-Markov process is reduced to ...The mean first-passage time of a bistable system with time-delayed feedback driven by multiplicative non-Gaussian noise and additive Gaussian white noise is investigated. Firstly, the non-Markov process is reduced to the Markov process through a path-integral approach; Secondly, the approximate Fokker-Planck equation is obtained by applying the unified coloured noise approximation, the small time delay approximation and the Novikov Theorem. The functional analysis and simplification are employed to obtain the approximate expressions of MFPT. The effects of non-Gaussian parameter （measures deviation from Gaussian character） r, the delay time τ, the noise correlation time to, the intensities D and a of noise on the MFPT are discussed. It is found that the escape time could be reduced by increasing the delay time τ, the noise correlation time τ0, or by reducing the intensities D and α. As far as we know, this is the first time to consider the effect of delay time on the mean first-passage time in the stochastic dynamical system.展开更多
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 p...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.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
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
The nonequilibrium phase transition and the symmetry revival induced by time delay in a bistable system are investigated. The stationary probability distribution function （SPDF） of the bistable system with time dela...The nonequilibrium phase transition and the symmetry revival induced by time delay in a bistable system are investigated. The stationary probability distribution function （SPDF） of the bistable system with time delay and correlated noises are calculated by an analytical method and stochastic simulation respectively. The analytical and simulative results indicate that： （1） There is a certain value of λ（λ denotes the strength of correlations between the multiplicative and additive noises） to make the SPDF symmetric under some time delay; however, above or below the given value, the symmetry will be broken; （2） With the monotonic change of λ, the unimodal peak structure of SPDF becomes bimodal at the beginning, then it becomes unimodal again; this means that there is a reentrance phenomenon in the process; （3） There is a critical value of delay time, which makes the lower peak of SPDF equal to the higher one under the critical condition. This means that the symmetry revival phenomenon emerges.展开更多
Coupling-induced logical stochastic resonance(LSR) can be observed in a noise-driven coupled bistable system where the behaviors of system can be interpreted consistently as a specific logic gate in an appropriate noi...Coupling-induced logical stochastic resonance(LSR) can be observed in a noise-driven coupled bistable system where the behaviors of system can be interpreted consistently as a specific logic gate in an appropriate noise level. Here constant coupling is extended to time-varying coupling, and then we investigate the effect of time-varying coupling on LSR in a periodically driven coupled bistable system. When coupling intensity oscillates periodically with the same frequency with periodic force or relatively high frequency, the system successfully yields the desired logic output. When coupling intensity oscillates irregularly with phase disturbance, large phase disturbance reduces the area of optimal parameter region of coupling intensity and response speed of logic devices. Although the system behaves as a desired logic gate when the frequency of time-periodic coupling intensity is precisely equal to that of periodic force, the desired logic gate is not robust against tiny frequency difference and phase disturbance. Therefore, periodic coupling intensity with high frequency ratio is an optimal option to obtain a reliable and robust logic operation.展开更多
In this paper, we discuss the effects of error feedback on the output of a nonlinear bistable system with stochastic resonance. The bit error rate is employed to quantify the performance of the system. The theoretical...In this paper, we discuss the effects of error feedback on the output of a nonlinear bistable system with stochastic resonance. The bit error rate is employed to quantify the performance of the system. The theoretical analysis and the numerical simulation are presented. By investigating the performances of the nonlinear systems with different strengths of error feedback, we argue that the presented system may provide guidance for practical nonlinear signal processing.展开更多
The phenomenon of stochastic resonance of a bistable system subjected to linear time-delayed feedback loops driven by multiplieative Gaussian coloured noise and additive Gaussian white noise is investigated. Firstly, ...The phenomenon of stochastic resonance of a bistable system subjected to linear time-delayed feedback loops driven by multiplieative Gaussian coloured noise and additive Gaussian white noise is investigated. Firstly, the analytic expression of the quasi-steady distribution function Ps （x, t） is derived by applying the unified coloured noise approximation and the Novikov Theorem; Secondly, the expression of the signal-to-noise ratio （SNR） is obtained in the adiabatic limit to quantify the stochastic resonance. Finally, tile effects of the linear coefficient a, the nonlinear coefficient b, the linear time-delayed feedback coefficient c and the delay time r on Ps（x,t） and SNR^± are discussed. It is found that the effects of the linear coefficient and the nonlinear coefficient, the positive linear time-delayed feedback coefficient and the negative linear time-delayed feedback coefficient, the positive delayed time and the negative delayed time on Ps（x,t） and SNR^± are different, respectively. This discussion would be helpful to the study of the system reliability and controlling stochastic resonance.展开更多
Effects of system size,coupling strength,and noise on vibrational resonance(VR)of globally coupled bistable systems are investigated.The power spectral amplifications obtained by the three methods all show that the VR...Effects of system size,coupling strength,and noise on vibrational resonance(VR)of globally coupled bistable systems are investigated.The power spectral amplifications obtained by the three methods all show that the VR exists over a wide range of parameter values.The increase in system size induces and enhances the VR,while the increase in noise intensity suppresses and eventually eliminates the VR.Both the stochastic resonance and the system size resonance can coexist with the VR in different parameter regions.This research has potential applications to the weak signal detection process in stochastic multi-body systems.展开更多
The effects of time delay on the fluctuation properties of a bistable system are investigated by simulating its normalised correlation function C（s）. Three cases including linear delay, cubic delay and global delay ...The effects of time delay on the fluctuation properties of a bistable system are investigated by simulating its normalised correlation function C（s）. Three cases including linear delay, cubic delay and global delay in the system are considered respectively. The simulation results indicate that the linear delay enhances the fluctuation of the system （reduces the stability of the system） while the cubic delay and global delay weaken it （enforce the stability of the system）, and the effect of cubic delay is more pronounced than the linear delay and global delay.展开更多
In this paper, we study the phenomenon of stochastic resonance （SR） in a periodically driven bistable system with correlations between multiplicative and additive white noise terms when there, are two different kind...In this paper, we study the phenomenon of stochastic resonance （SR） in a periodically driven bistable system with correlations between multiplicative and additive white noise terms when there, are two different kinds of time delays existed in the deterministic and fluctuating forces, respectively. Using the small time delay approximation and the theory of signal-to-noise ratio （SNR） in the adiabatic limit, the expression of SNR is obtained. The effects of the delay time T in the deterministic force, and the delay time 8 in the fluctuating force on SNR are discussed. Based on the numerical computation, it is found that： （i） There appears a reentrant transition between one peak and two peaks and then to one peak again in the curve of SNR when the value of the time delay θ is increased. （ii） SR can be realized by tuning the time delay T or 8 with fixed noise, i.e., delay-induced stochastic resonance （DSR） exists.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
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
The effects of the correlation time τ between noises on the noise-enhanced stability （NES） phe- nomenon in an asymmetric bistable system driven by cross-correlated noise are investigated. The ex- pressions for the ...The effects of the correlation time τ between noises on the noise-enhanced stability （NES） phe- nomenon in an asymmetric bistable system driven by cross-correlated noise are investigated. The ex- pressions for the average escape time from the left metastable state TL and from the right metastable state TR are derived. The results indicate that： i） The NES effect is suppressed as the correlation time τ increases for two metastable states; ii） The increase in τ speeds up the escape process from the right state for positively correlated noise, whereas its role is reverses for negatively correlated; iii） In the escape process from the left state, the role of τ is opposite to that in escape from the right state.展开更多
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 supported by the National Natural Science Foundation of China(Grant No.11772048)
文摘Stochastic resonance（SR） is studied in an under-damped bistable system driven by the harmonic mixing signal and Gaussian white noise. Using the linear response theory（LRT）, the expressions of the spectral amplification at fundamental and higher-order harmonic are obtained. The effects of damping coefficient, noise intensity, signal amplitude, and frequency on spectral amplifications are explored. Meanwhile, the power spectral density（PSD） and signal-to-noise ratio（SNR） are calculated to quantify SR and verify the theoretical results. The SNRs at the first and second harmonics exhibit a minimum first and a maximum later with increasing noise intensity. That is, both of the noise-induced suppression and resonance can be observed by choosing proper system parameters. Especially, when the ratio of the second harmonic amplitude to the fundamental one takes a large value, the SNR at the fundamental harmonic is a monotonic function of noise intensity and the SR phenomenon disappears.
基金Project supported by the National Nature Science Foundation of China （Grant No 10363001） and the project of Baoji University of Sciences and Arts of China （Grant No ZK2508）.
文摘The steady-state properties of a bistable system are investigated when both the multiplicative noise and the coupling between additive and multiplicative noises are coloured with different values of noise correlation times T1 and T2. After introducing a dimensionless parameter R（R = α/D, D is the intensity of the multiplicative noise and a is the intensity of the additive noise）, and performing the numerical computations, we find the following points： （1） For the case of R 〉 1, A （the intensity of correlation between additive and multiplicative noises）, T1 and T2 can induce the stationary probability distribution （SPD） transition from bimodal to unimodal in structure, but for the cases of R _〈 1, the bimodal structure is preserved; （2） a can also induce the SPD transition from bimodal to unimodal in structure; （3） the bimodal structure of the SPD exhibits a symmetrical structure as D increases.
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 Natural Science Foundation of China under Grant No.10865006the Natural Science Foundation of Shaanxi Province under Grant No.2010JQ1014the Science Foundation of Baoji University of Science and Arts of China under Grant No.ZK0954
文摘The asymmetric effects on the escape rates from the stable states x±in the bistable system are analyzed. The results indicate that the multiplicative noise and the additive noise always enhance the particle escape from stable states x±of bistable.However,the asymmetric parameter r enhances the particle escape from stable state x_+,and holds back the particle escape from stable state x_-.
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National Natural Science Foundation of China under Grant Nos.10472091,10332030,and 10502042
文摘The mean first-passage time of a bistable system with time-delayed feedback driven by multiplicative non-Gaussian noise and additive Gaussian white noise is investigated. Firstly, the non-Markov process is reduced to the Markov process through a path-integral approach; Secondly, the approximate Fokker-Planck equation is obtained by applying the unified coloured noise approximation, the small time delay approximation and the Novikov Theorem. The functional analysis and simplification are employed to obtain the approximate expressions of MFPT. The effects of non-Gaussian parameter （measures deviation from Gaussian character） r, the delay time τ, the noise correlation time to, the intensities D and a of noise on the MFPT are discussed. It is found that the escape time could be reduced by increasing the delay time τ, the noise correlation time τ0, or by reducing the intensities D and α. As far as we know, this is the first time to consider the effect of delay time on the mean first-passage time in the stochastic dynamical system.
基金supported by the National Natural Science Foundation of China(Grant No 50675214)Natural Science Foundation of Zhejiang Province of China(Grant No Y7080111)
文摘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.
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 No 10865006)
文摘The nonequilibrium phase transition and the symmetry revival induced by time delay in a bistable system are investigated. The stationary probability distribution function （SPDF） of the bistable system with time delay and correlated noises are calculated by an analytical method and stochastic simulation respectively. The analytical and simulative results indicate that： （1） There is a certain value of λ（λ denotes the strength of correlations between the multiplicative and additive noises） to make the SPDF symmetric under some time delay; however, above or below the given value, the symmetry will be broken; （2） With the monotonic change of λ, the unimodal peak structure of SPDF becomes bimodal at the beginning, then it becomes unimodal again; this means that there is a reentrance phenomenon in the process; （3） There is a critical value of delay time, which makes the lower peak of SPDF equal to the higher one under the critical condition. This means that the symmetry revival phenomenon emerges.
基金supported by the National Natural Science Foundation of China (Grant No. 31601071)。
文摘Coupling-induced logical stochastic resonance(LSR) can be observed in a noise-driven coupled bistable system where the behaviors of system can be interpreted consistently as a specific logic gate in an appropriate noise level. Here constant coupling is extended to time-varying coupling, and then we investigate the effect of time-varying coupling on LSR in a periodically driven coupled bistable system. When coupling intensity oscillates periodically with the same frequency with periodic force or relatively high frequency, the system successfully yields the desired logic output. When coupling intensity oscillates irregularly with phase disturbance, large phase disturbance reduces the area of optimal parameter region of coupling intensity and response speed of logic devices. Although the system behaves as a desired logic gate when the frequency of time-periodic coupling intensity is precisely equal to that of periodic force, the desired logic gate is not robust against tiny frequency difference and phase disturbance. Therefore, periodic coupling intensity with high frequency ratio is an optimal option to obtain a reliable and robust logic operation.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61171147 and 60702022)
文摘In this paper, we discuss the effects of error feedback on the output of a nonlinear bistable system with stochastic resonance. The bit error rate is employed to quantify the performance of the system. The theoretical analysis and the numerical simulation are presented. By investigating the performances of the nonlinear systems with different strengths of error feedback, we argue that the presented system may provide guidance for practical nonlinear signal processing.
基金supported by National Natural Science Foundation of China under Grant Nos.10472091 and 10332030
文摘The phenomenon of stochastic resonance of a bistable system subjected to linear time-delayed feedback loops driven by multiplieative Gaussian coloured noise and additive Gaussian white noise is investigated. Firstly, the analytic expression of the quasi-steady distribution function Ps （x, t） is derived by applying the unified coloured noise approximation and the Novikov Theorem; Secondly, the expression of the signal-to-noise ratio （SNR） is obtained in the adiabatic limit to quantify the stochastic resonance. Finally, tile effects of the linear coefficient a, the nonlinear coefficient b, the linear time-delayed feedback coefficient c and the delay time r on Ps（x,t） and SNR^± are discussed. It is found that the effects of the linear coefficient and the nonlinear coefficient, the positive linear time-delayed feedback coefficient and the negative linear time-delayed feedback coefficient, the positive delayed time and the negative delayed time on Ps（x,t） and SNR^± are different, respectively. This discussion would be helpful to the study of the system reliability and controlling stochastic resonance.
基金Project supported by the Xing Dian Talents Support Project of Yunnan Province(Grant No.YNWR-QNBJ-2018-0040)the Youth Project of Applied Basic Research of Yunnan Science(Grant No.202201AU070062)the Yunnan University’s Research Innovation Fund for Graduate Students(Grant No.KC-22221171).
文摘Effects of system size,coupling strength,and noise on vibrational resonance(VR)of globally coupled bistable systems are investigated.The power spectral amplifications obtained by the three methods all show that the VR exists over a wide range of parameter values.The increase in system size induces and enhances the VR,while the increase in noise intensity suppresses and eventually eliminates the VR.Both the stochastic resonance and the system size resonance can coexist with the VR in different parameter regions.This research has potential applications to the weak signal detection process in stochastic multi-body systems.
基金Project supported by the National Natural Science Foundation of China(Grant No.10865006)the Science Foundation of Yunnan University(Grant No.2009A01z)the Graduate Science Foundation of Yunnan University(Grant No.ynuy200926)
文摘The effects of time delay on the fluctuation properties of a bistable system are investigated by simulating its normalised correlation function C（s）. Three cases including linear delay, cubic delay and global delay in the system are considered respectively. The simulation results indicate that the linear delay enhances the fluctuation of the system （reduces the stability of the system） while the cubic delay and global delay weaken it （enforce the stability of the system）, and the effect of cubic delay is more pronounced than the linear delay and global delay.
基金Supported by the Natural Science Foundation of Yunnan Province under Grant No.08C0235
文摘In this paper, we study the phenomenon of stochastic resonance （SR） in a periodically driven bistable system with correlations between multiplicative and additive white noise terms when there, are two different kinds of time delays existed in the deterministic and fluctuating forces, respectively. Using the small time delay approximation and the theory of signal-to-noise ratio （SNR） in the adiabatic limit, the expression of SNR is obtained. The effects of the delay time T in the deterministic force, and the delay time 8 in the fluctuating force on SNR are discussed. Based on the numerical computation, it is found that： （i） There appears a reentrant transition between one peak and two peaks and then to one peak again in the curve of SNR when the value of the time delay θ is increased. （ii） SR can be realized by tuning the time delay T or 8 with fixed noise, i.e., delay-induced stochastic resonance （DSR） exists.
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.
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This work was supported by the National Natural Science Foundation of China （Grant No. 11165016）, the Key Project of Research Fund of Education Department of Yunnan Province （Grant No. 2013Z097） and the Natural Science Founda- tion of Yunnan Province of China （Grant No. 2012FB176）.
文摘The effects of the correlation time τ between noises on the noise-enhanced stability （NES） phe- nomenon in an asymmetric bistable system driven by cross-correlated noise are investigated. The ex- pressions for the average escape time from the left metastable state TL and from the right metastable state TR are derived. The results indicate that： i） The NES effect is suppressed as the correlation time τ increases for two metastable states; ii） The increase in τ speeds up the escape process from the right state for positively correlated noise, whereas its role is reverses for negatively correlated; iii） In the escape process from the left state, the role of τ is opposite to that in escape from the right state.
