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 investigates the stochastic resonance （SR） induced by a multiplicative periodic signal in the gene transcriptional regulatory system with correlated noises. The expression of the signal-to-noise ratio （...This paper investigates the stochastic resonance （SR） induced by a multiplicative periodic signal in the gene transcriptional regulatory system with correlated noises. The expression of the signal-to-noise ratio （SNR） is derived. The results indicate that the existence of a maximum in SNR vs. the additive noise intensity α the multiplicative noise intensity D and the cross-correlated noise intensity λ is the identifying characteristic of the SR phenomenon and there is a critical phenomenon in the SNR as a function of λ, i.e., for the case of smaller values of noise intensity （α or D）, the SNR decreases as λ increases; however, for the case of larger values of noise intensity （α or D）, the SNR increases as λ increases.展开更多
The phenomenon of stochastic resonance （SR） in the tumour cell growth model subjected cross-correlated noises is investigated. When a weakly periodic signal is added to the system, the signal-to-noise ratio RSNR is ...The phenomenon of stochastic resonance （SR） in the tumour cell growth model subjected cross-correlated noises is investigated. When a weakly periodic signal is added to the system, the signal-to-noise ratio RSNR is derived by the quasi-steady-state probability distribution function and the adiabatic elimination method. Based on the derived RSNR, the effects of these parameters （the cross-correlated strength λ and the cross-correlated time τ） are analysed by numerical calculation. It is found that the existence of a maximum in RSNR is the identifying characteristic of the SR phenomenon. The maximum of RsNR decreases with the increase of λ and increases with the increase of τ.展开更多
The transient properties of a bistable system driven by cross-correlated noises are investigated,the correlation times of the correlations between the noises are nonzero.The explicit expression of the mean,first-passa...The transient properties of a bistable system driven by cross-correlated noises are investigated,the correlation times of the correlations between the noises are nonzero.The explicit expression of the mean,first-passage time(MFPT)is obtained.From numerical computations we find the following.(1)The MFPT of the system is affected by the correlation time T and the correlation strength λ,T and λ play opposing roles in the MFPT.(2)For the case of perfectly correlated noises(λ=1),the MFPT corresponding to α>D and α<D(α and D are the additive noise and multiplicative noise intensities,respectively)exhibit the same behaviors and the MFPT for α=D is continuous,which is very different from the case of τ=0[Phys.Rev.E 53(1996)5764].展开更多
The time-delayed bistable system subjected to the multiplicative and additive noises is investigated. In the condition of small delay time, the stationary probability distribution function （SPDF） is derived, and und...The time-delayed bistable system subjected to the multiplicative and additive noises is investigated. In the condition of small delay time, the stationary probability distribution function （SPDF） is derived, and under the condition of large delay time, the SPDF is stochastically simulated. The analytical and simulative results indicate that： （i） For the case of λ = 0 （λ denotes the strength of correlations between the multiplicative and additive noises）, the time delay affects weakly the SPDF peak structure, and the symmetrical property of the SPDF two-peak structure does not change with the increasing delay time. （ii） For the case of λ≠0, the two-peak structure changes with the increasing delay time, i.e. one peak goes up and the other go down simultaneously as the delay time increases and along with further increase of the delay time, the lower peak disappears gradually while the higher one goes up, i.e. the structure of the SPDF changes from a bimodal to a unimodal and the system becomes monostable.展开更多
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 National Natural Science Foundation of China (Grant No.10865006)the Science Foundation of Yunnan University (Grant No.2009A01Z)
文摘This paper investigates the stochastic resonance （SR） induced by a multiplicative periodic signal in the gene transcriptional regulatory system with correlated noises. The expression of the signal-to-noise ratio （SNR） is derived. The results indicate that the existence of a maximum in SNR vs. the additive noise intensity α the multiplicative noise intensity D and the cross-correlated noise intensity λ is the identifying characteristic of the SR phenomenon and there is a critical phenomenon in the SNR as a function of λ, i.e., for the case of smaller values of noise intensity （α or D）, the SNR decreases as λ increases; however, for the case of larger values of noise intensity （α or D）, the SNR increases as λ increases.
基金Supported by the Natural Science Foundation of Yunnan Province under Grant No 2006A0002M.
文摘The phenomenon of stochastic resonance （SR） in the tumour cell growth model subjected cross-correlated noises is investigated. When a weakly periodic signal is added to the system, the signal-to-noise ratio RSNR is derived by the quasi-steady-state probability distribution function and the adiabatic elimination method. Based on the derived RSNR, the effects of these parameters （the cross-correlated strength λ and the cross-correlated time τ） are analysed by numerical calculation. It is found that the existence of a maximum in RSNR is the identifying characteristic of the SR phenomenon. The maximum of RsNR decreases with the increase of λ and increases with the increase of τ.
基金Supported by the National Natural Science Foundation of China under Grant No.19863001the Applied Basic Research Foundations of Yunnan Province and Yunnan Education Committee.
文摘The transient properties of a bistable system driven by cross-correlated noises are investigated,the correlation times of the correlations between the noises are nonzero.The explicit expression of the mean,first-passage time(MFPT)is obtained.From numerical computations we find the following.(1)The MFPT of the system is affected by the correlation time T and the correlation strength λ,T and λ play opposing roles in the MFPT.(2)For the case of perfectly correlated noises(λ=1),the MFPT corresponding to α>D and α<D(α and D are the additive noise and multiplicative noise intensities,respectively)exhibit the same behaviors and the MFPT for α=D is continuous,which is very different from the case of τ=0[Phys.Rev.E 53(1996)5764].
基金Supported by the Natural Science Foundation of Yun Province under Grant No 2006A0002M
文摘The time-delayed bistable system subjected to the multiplicative and additive noises is investigated. In the condition of small delay time, the stationary probability distribution function （SPDF） is derived, and under the condition of large delay time, the SPDF is stochastically simulated. The analytical and simulative results indicate that： （i） For the case of λ = 0 （λ denotes the strength of correlations between the multiplicative and additive noises）, the time delay affects weakly the SPDF peak structure, and the symmetrical property of the SPDF two-peak structure does not change with the increasing delay time. （ii） For the case of λ≠0, the two-peak structure changes with the increasing delay time, i.e. one peak goes up and the other go down simultaneously as the delay time increases and along with further increase of the delay time, the lower peak disappears gradually while the higher one goes up, i.e. the structure of the SPDF changes from a bimodal to a unimodal and the system becomes monostable.
