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The effects of time delay on transition rate from metastable state to stable state in a Logistic system are investigated. On the assumption that there is a delay time in the decay process of cell evolution, the expression of the transition rate is derived in the first order approximation under the condition of the small delay time and the steepest-descent approximation. The numerically calculated results indicate that the additive noise, the multiplicative noise and the correlations between additive and multiplicative noises enhance the system transition from metastable state to stable state. However, such a transition is restrained by the time delay, i.e., the time delay enhances the stability of the system.
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Keywords:
- Logistic model /
- transition rate /
- time delay /
- noise
[1] Ai B Q, Wang X J, Liu G T, Liu L G 2003 Phys. Rev. E 67 022903
[2] Mei D C, Xie C W, Zhang L 2004 Eur. Phys. J. B 41 107
[3] Cai J C, Wang C J, Mei D C 2007 Chin. Phys. Lett. 24 1162
[4] Bai C Y, Du L C, Mei D C 2009 Cent. Eur. J. Phys. 7 601
[5] Wang C J, Wei Q, Zheng B B, Mei D C 2008 Acta Phys. Sin. 57 1375(in Chinese)[王参军、魏 群、郑宝兵、梅冬成 2008 物理学报 57 1375]
[6] Wang C J, Wei Q, Mei D C 2008 Phys. Lett. A 3722176
[7] Wu D, Zhu S Q2006 Phys. Rev. E 73 051107
[8] Nie L R, Mei D C2007 Europhysics Letters 79 20005
[9] Nie L R, Mei D C2008 Phys. Rev. E 77 031107
[10] Du L C,Mei D C 2010 Phys.Lett. A 374 3275
[11] Han L B 2008 Acta Phys. Sin. 57 2699 (in Chinese)[韩立波 2008 物理学报 57 2699]
[12] Li L, Yan Y, Mei D C 2010 Acta Phys. Sin. 59 2240(in Chinese)[林 灵、闫 勇、梅冬成 2010 物理学报 59 2240]
[13] Frank T D 2005 Phys. Rev. E 71 031106
[14] H|nggi P, Talkner P 1983 Phys. Rev. Lett. 51 2242
[15] Guardia E, Miguel M S 1985 Phys. Lett. A 109 9
[16] Madureira A J R, Hönggi P, Wio H S 1996 Phys. Lett. A 217 248
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[1] Ai B Q, Wang X J, Liu G T, Liu L G 2003 Phys. Rev. E 67 022903
[2] Mei D C, Xie C W, Zhang L 2004 Eur. Phys. J. B 41 107
[3] Cai J C, Wang C J, Mei D C 2007 Chin. Phys. Lett. 24 1162
[4] Bai C Y, Du L C, Mei D C 2009 Cent. Eur. J. Phys. 7 601
[5] Wang C J, Wei Q, Zheng B B, Mei D C 2008 Acta Phys. Sin. 57 1375(in Chinese)[王参军、魏 群、郑宝兵、梅冬成 2008 物理学报 57 1375]
[6] Wang C J, Wei Q, Mei D C 2008 Phys. Lett. A 3722176
[7] Wu D, Zhu S Q2006 Phys. Rev. E 73 051107
[8] Nie L R, Mei D C2007 Europhysics Letters 79 20005
[9] Nie L R, Mei D C2008 Phys. Rev. E 77 031107
[10] Du L C,Mei D C 2010 Phys.Lett. A 374 3275
[11] Han L B 2008 Acta Phys. Sin. 57 2699 (in Chinese)[韩立波 2008 物理学报 57 2699]
[12] Li L, Yan Y, Mei D C 2010 Acta Phys. Sin. 59 2240(in Chinese)[林 灵、闫 勇、梅冬成 2010 物理学报 59 2240]
[13] Frank T D 2005 Phys. Rev. E 71 031106
[14] H|nggi P, Talkner P 1983 Phys. Rev. Lett. 51 2242
[15] Guardia E, Miguel M S 1985 Phys. Lett. A 109 9
[16] Madureira A J R, Hönggi P, Wio H S 1996 Phys. Lett. A 217 248
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