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The time-delay effect of a genotype selection model driven by noise is investigated. The approximate delay Fokker-Planck equation is obtained based on the small time delay method and the stochastic equivalent rule. The explicit expression of the steady state probability distribution is derived, and the effect of the time delay on the steady sate properties of the genotype selection model driven by noise is discussed. It is found that the time delay can induce the transition from monostable state to bistable state. The time delay is helpful to select one type of genes from another type of mixing genes. The theoretical predictions are found to be in basic agreement with numerical results.
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Keywords:
- time delay /
- noise /
- genotype selection model /
- transition
[1] Ohira T, Milton J G 1995 Phys. Rev. E 52 3277
[2] Tsimring L, Pikovsky A 2001 Phys. Rev. Lett. 87 250602
[3] Houlihan J, Goulding D, Busch T,Masoller C, Huyet G 2004 Phys. Rev. Lett. 92 050601
[4] Masoller C 2003 Phys. Rev. Lett. 90 020601
[5] Huber D, Tsimzing L 2003 Phys. Rev. Lett. 91 260601
[6] Piwonski T, Houlihan J, Busch T, Huyet G 2005 Phys. Rev. Lett. 95 040601
[7] Lin L, Yan Y, Mei D C 2010 Acta Phys. Sin. 59 2240 (in Chinese) [林灵, 闫勇, 梅冬成 2010 59 2240]
[8] Ying Y J, Huang Z Q 2001 Chin. Phys. Lett. 18 695
[9] Dhamala M, Jirsa V K, Ding M 2004 Phys. Rev. Lett. 92 028101
[10] Dhamala M, Jirsa V K, Ding M 2004 Phys. Rev. Lett. 92 074104
[11] Wu D, Zhu S 2006 Phys. Rev. E 73 051107
[12] Nie L R, Mei D C 2007 Eur. Phys. Lett. 79 20005
[13] Li J C, Mei D C 2008 Acta Phys. Sin. 57 6792 (in Chinese) [李江城, 梅冬成 2008 57 6792]
[14] Yang L J 2011 Acta Phys. Sin. 60 050502 (in Chinese) [杨林静 2011 60 050502]
[15] Wang J Y, Zhu C L, Jia Y, Li J R 2006 Chin. Phys. Lett. 23 1398
[16] Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Science and Technological Education Publishing House) p163-168 (in Chinese) [胡岗 1994 随机力与非线性系统 (第1版) (上海: 上海科技教育出版社) 第163-168页]
[17] Horsthemke W, Lefever R 1984 Noise-Induced Transitions: Theory and Applications in Physics, Chemistry, and Biology (Berlin: Springer-Verlag)
[18] Ai B Q, Chen W, Wang X J, Liu G T, Wen D H, Liu L G 2003 Commun. Theor. Phys. 39 765
[19] Zhang L, Cao L 2010 Chin. Phys. Lett. 27 060504
[20] Wang C J, Mei D C 2008 Chin. Phys. B 17 479
[21] Castro F, S?anchez A D, Wio H S 1995 Phys. Rev. Lett. 75 1691
[22] Soldatov A V 1993 Mod. Phys. Lett. B 7 1253
[23] Zhang X M, Ai B Q 2010 Eur. Phys. J. B 73 433
[24] Wio H S, Toral R 2004 Physica D 193 161
[25] Wu D J, Cao L, Ke S Z 1994 Phys. Rev. E 50 2496
[26] Cao L, Wu D J, Ke S Z 1995 Phys. Rev. E 52 3228
[27] Guillouzic S, L'Heureux I, Longtin A 1999 Phys. Rev. E 59 3970
[28] Guillouzic S, L'Heureux I, Longtin A 2000 Phys. Rev. E 61 4906
[29] Wu D, Zhu S Q 2007 Phys. Lett. A 363 202
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[1] Ohira T, Milton J G 1995 Phys. Rev. E 52 3277
[2] Tsimring L, Pikovsky A 2001 Phys. Rev. Lett. 87 250602
[3] Houlihan J, Goulding D, Busch T,Masoller C, Huyet G 2004 Phys. Rev. Lett. 92 050601
[4] Masoller C 2003 Phys. Rev. Lett. 90 020601
[5] Huber D, Tsimzing L 2003 Phys. Rev. Lett. 91 260601
[6] Piwonski T, Houlihan J, Busch T, Huyet G 2005 Phys. Rev. Lett. 95 040601
[7] Lin L, Yan Y, Mei D C 2010 Acta Phys. Sin. 59 2240 (in Chinese) [林灵, 闫勇, 梅冬成 2010 59 2240]
[8] Ying Y J, Huang Z Q 2001 Chin. Phys. Lett. 18 695
[9] Dhamala M, Jirsa V K, Ding M 2004 Phys. Rev. Lett. 92 028101
[10] Dhamala M, Jirsa V K, Ding M 2004 Phys. Rev. Lett. 92 074104
[11] Wu D, Zhu S 2006 Phys. Rev. E 73 051107
[12] Nie L R, Mei D C 2007 Eur. Phys. Lett. 79 20005
[13] Li J C, Mei D C 2008 Acta Phys. Sin. 57 6792 (in Chinese) [李江城, 梅冬成 2008 57 6792]
[14] Yang L J 2011 Acta Phys. Sin. 60 050502 (in Chinese) [杨林静 2011 60 050502]
[15] Wang J Y, Zhu C L, Jia Y, Li J R 2006 Chin. Phys. Lett. 23 1398
[16] Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Science and Technological Education Publishing House) p163-168 (in Chinese) [胡岗 1994 随机力与非线性系统 (第1版) (上海: 上海科技教育出版社) 第163-168页]
[17] Horsthemke W, Lefever R 1984 Noise-Induced Transitions: Theory and Applications in Physics, Chemistry, and Biology (Berlin: Springer-Verlag)
[18] Ai B Q, Chen W, Wang X J, Liu G T, Wen D H, Liu L G 2003 Commun. Theor. Phys. 39 765
[19] Zhang L, Cao L 2010 Chin. Phys. Lett. 27 060504
[20] Wang C J, Mei D C 2008 Chin. Phys. B 17 479
[21] Castro F, S?anchez A D, Wio H S 1995 Phys. Rev. Lett. 75 1691
[22] Soldatov A V 1993 Mod. Phys. Lett. B 7 1253
[23] Zhang X M, Ai B Q 2010 Eur. Phys. J. B 73 433
[24] Wio H S, Toral R 2004 Physica D 193 161
[25] Wu D J, Cao L, Ke S Z 1994 Phys. Rev. E 50 2496
[26] Cao L, Wu D J, Ke S Z 1995 Phys. Rev. E 52 3228
[27] Guillouzic S, L'Heureux I, Longtin A 1999 Phys. Rev. E 59 3970
[28] Guillouzic S, L'Heureux I, Longtin A 2000 Phys. Rev. E 61 4906
[29] Wu D, Zhu S Q 2007 Phys. Lett. A 363 202
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