摘要We study the stochastic resonance (SR) phenomenon in a time-delayed gene transcriptional regulatory system under the simultaneous action of a multiplicative noise and an additive noise and a weak periodic signal. The expression of the signal-to-noise ratio RSNR is obtained by applying the two-state theory in adiabatic limit under the condition of small delay time. The effects of delay time and intensity of the correlation between multiplicative and additive noise on RSNR are discussed. It is found that the delay time τ enhances the SR of the system. The correlation intensity λ enhances the SR in the RSNR-D plot (D denotes the multiplicative noise intensity), but weakens the SR in the RSNR-α plot (α denotes the additive noise intensity).
Abstract:We study the stochastic resonance (SR) phenomenon in a time-delayed gene transcriptional regulatory system under the simultaneous action of a multiplicative noise and an additive noise and a weak periodic signal. The expression of the signal-to-noise ratio RSNR is obtained by applying the two-state theory in adiabatic limit under the condition of small delay time. The effects of delay time and intensity of the correlation between multiplicative and additive noise on RSNR are discussed. It is found that the delay time τ enhances the SR of the system. The correlation intensity λ enhances the SR in the RSNR-D plot (D denotes the multiplicative noise intensity), but weakens the SR in the RSNR-α plot (α denotes the additive noise intensity).
ZENG Chun-Hua;XIE Chong-Wei. Stochastic Resonance in a Gene Transcriptional Regulatory System with Time Delay[J]. 中国物理快报, 2008, 25(5): 1587-1590.
ZENG Chun-Hua, XIE Chong-Wei. Stochastic Resonance in a Gene Transcriptional Regulatory System with Time Delay. Chin. Phys. Lett., 2008, 25(5): 1587-1590.
[1] Benzi R, Sutera A and Vulpiani A 1981 J. Phys. A 14 L453 [2] Nicolis C and Nicolis G 1981 Tellus 33 225 [3] Fauve S and Heslot F 1983 Phys. Lett. A 97 5 [4] McNamara B, Wiesenfeld K and Roy R 1989 Phys. Rev.Lett 60 2626 [5] McNamara B and Wiesenfeld K 1989 Phys. Rev. A 39 4854 [6] Frank T D 2005 Phys. Rev. E 71 031106 [7] Frank T D 2005 Phys. Rev. E 72 011112 [8] Jin Y F and Hu H Y 2007 Physica A 382 423 [9] Wu D and Zhu S Q 2007 Phys. Lett. A 363 202 [10] Masoller C 2002 Phys. Rev. Lett 88 034102 [11] Nie L R and Mei D C 2007 Europhys. Lett. 7920005 [12] Liu Q and Jia Y 2004 Phys. Rev. E 70 041907 [13] Smolen P, Baxter D A and Byrne J H 1998 Am. J.Physiol. C 274 531 [14] Wang J Y, Zhu C L, Jia Y and Li R L 2006 Chin. Phys.Leet 20 1398 [15] Li J H and Huang Z Q 1996 Phys. Rev. E 533315 [16] Wu D J, Cao L and Ke S Z 1994 Phys. Rev. E 502496 [17] Jia Y and Li J R 1996 Phys. Rev. E 53 5764 [18] Mei D C, Xie G Z, Cao L and Wu D J 1999 Phys. Rev.E 59 3880 [19] Madureira A J R, Hanggi and Wio H S 1996 Phys.Lett. A 217 248 [20] Gammaitoni L, Hanggi P, Jung P and Marchesoni F 1998 Rev. Mod. Phys 70 224