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Effects of time delay on the active rate of a bistable system was investigated. Using the steepest-descent approximation method, the analytical expression of the mean first passage time and the active rate of the bistable system with time delay was derived under the condition of small delay time. The numerical computations show that the time delay enhances the resonance suppression in the system.
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Keywords:
- bistable system /
- time delay /
- resonance suppression
[1] ［1］Niebur E, Schuster H G, Kammen D M 1991 Phys. Rev. Lett. 67 2753
[2] ［2］Losson J, Mackey M C 1995 Phys. Rev. E 52 115
[3] ［3］Boccaletti S, Maza D, Mancini H, Genesio R, Arecchi F T 1997 Phys. Rev. Lett. 79 5246
[4] ［4］Yeung M K S, Strogatz S H 1999 Phys. Rev. Lett. 82 648
[5] ［5］Li J C, Mei D C 2008 Acta Phys. Sin. 57 6792 (in Chinese) ［李江城、梅冬成 2008 物理学报 57 6792］
[6] ［6］Janson N B, Balanov A G, Schll E 2004 Phys. Rev. Lett. 93 010601
[7] ［7］Balanov A G, Beato V, Janson N B, Engel H, Schll E 2006 Phys. Rev. E 74 016214
[8] ［8］Zhang T R 2007 Statistical Dynamics and Application (Beijing: Metallurgical Industry Press ) p13
[9] (in Chinese) ［张太荣 2007 统计动力学及其应用 (北京：冶金工业出版社) 第13页］
[10] ［9］Hu G 1994 Stochastic Force and Nonlinear System (Shanghai: Shanghai Scientific and Technological Education Publishing House) p5 (in Chinese) ［胡岗 1994 随机力与非线性系统(上海: 上海科技教育出版社) 第5页］
[11] ］Ohira T, Milton J G 1995 Phys. Rev. E 52 3277
[12] ］Ying Y J, Huang Z Q 2001 Chin. Phys. Lett. 18 695
[13] ］Wu D, Zhu S Q 2006 Phys. Rev. E 73 051107
[14] ］Nie L R, Mei D C 2007 Europhys. Lett. 79 20005
[15] ］Guillouzic S, L′Heureux I, Longtin A 1999 Phys. Rev. E 59 3970
[16] ］Frank T D 2005 Phys. Rev. E 72 011112
[17] ］Tsimring L, Pikovsky A 2001 Phys. Rev. Lett. 87 250602
[18] ］Madureira A J R, Hanggi P, Wio H S 1996 Phys. Lett. A 217 248
[19] ］Wu D J, Cao L, Ke S Z 1994 Phys. Rev. E 50 2496
[20] ］Jia Y, Li J R 1996 Phys. Rev. E 53 5786
[21] ］Jia Y, Li J R 1996 Phys. Rev. E 53 5764
[22] ］Jia Y, Li J R 1997 Phys. Rev. Lett. 78 994
[23] ］Mei D C, Xie C W, Zhang L 2003 Phys. Rev. E 68 051102
[24] ］Mei D C, Xie G Z, Cao L, Wu D J 1999 Phys. Rev. E 59 3880
[25] ］Mei D C, Xie G Z, Cao L, Wu D J 1999 Chin. Phys. Lett. 16 327
[26] ］Xie C W, Mei D C 2003 Chin. Phys. Lett. 20 813
[27] ］Wang C J, Mei D C 2006 Chin. Phys. 15 1435
[28] ］Mei D C, Xie C W, Xiang Y L 2004 Physica A 343 167
[29] ］Shao J H, Wang B, Wu X Q 2009 Acta Phys. Sin. 58 1391 (in Chinese) ［邵继红、王兵、吴秀清 2009 物理学报 58 1391］
[30] ］Wu D, Zhu S Q 2007 Phys. Lett. A 363 202
[31] ］Nie L R, Mei D C 2007 Chin. Phys. Lett. 24 3074
[32] ］Wang C J, Mei D C 2008 Mod. Phys. Lett. B 22 2677
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[1] ［1］Niebur E, Schuster H G, Kammen D M 1991 Phys. Rev. Lett. 67 2753
[2] ［2］Losson J, Mackey M C 1995 Phys. Rev. E 52 115
[3] ［3］Boccaletti S, Maza D, Mancini H, Genesio R, Arecchi F T 1997 Phys. Rev. Lett. 79 5246
[4] ［4］Yeung M K S, Strogatz S H 1999 Phys. Rev. Lett. 82 648
[5] ［5］Li J C, Mei D C 2008 Acta Phys. Sin. 57 6792 (in Chinese) ［李江城、梅冬成 2008 物理学报 57 6792］
[6] ［6］Janson N B, Balanov A G, Schll E 2004 Phys. Rev. Lett. 93 010601
[7] ［7］Balanov A G, Beato V, Janson N B, Engel H, Schll E 2006 Phys. Rev. E 74 016214
[8] ［8］Zhang T R 2007 Statistical Dynamics and Application (Beijing: Metallurgical Industry Press ) p13
[9] (in Chinese) ［张太荣 2007 统计动力学及其应用 (北京：冶金工业出版社) 第13页］
[10] ［9］Hu G 1994 Stochastic Force and Nonlinear System (Shanghai: Shanghai Scientific and Technological Education Publishing House) p5 (in Chinese) ［胡岗 1994 随机力与非线性系统(上海: 上海科技教育出版社) 第5页］
[11] ］Ohira T, Milton J G 1995 Phys. Rev. E 52 3277
[12] ］Ying Y J, Huang Z Q 2001 Chin. Phys. Lett. 18 695
[13] ］Wu D, Zhu S Q 2006 Phys. Rev. E 73 051107
[14] ］Nie L R, Mei D C 2007 Europhys. Lett. 79 20005
[15] ］Guillouzic S, L′Heureux I, Longtin A 1999 Phys. Rev. E 59 3970
[16] ］Frank T D 2005 Phys. Rev. E 72 011112
[17] ］Tsimring L, Pikovsky A 2001 Phys. Rev. Lett. 87 250602
[18] ］Madureira A J R, Hanggi P, Wio H S 1996 Phys. Lett. A 217 248
[19] ］Wu D J, Cao L, Ke S Z 1994 Phys. Rev. E 50 2496
[20] ］Jia Y, Li J R 1996 Phys. Rev. E 53 5786
[21] ］Jia Y, Li J R 1996 Phys. Rev. E 53 5764
[22] ］Jia Y, Li J R 1997 Phys. Rev. Lett. 78 994
[23] ］Mei D C, Xie C W, Zhang L 2003 Phys. Rev. E 68 051102
[24] ］Mei D C, Xie G Z, Cao L, Wu D J 1999 Phys. Rev. E 59 3880
[25] ］Mei D C, Xie G Z, Cao L, Wu D J 1999 Chin. Phys. Lett. 16 327
[26] ］Xie C W, Mei D C 2003 Chin. Phys. Lett. 20 813
[27] ］Wang C J, Mei D C 2006 Chin. Phys. 15 1435
[28] ］Mei D C, Xie C W, Xiang Y L 2004 Physica A 343 167
[29] ］Shao J H, Wang B, Wu X Q 2009 Acta Phys. Sin. 58 1391 (in Chinese) ［邵继红、王兵、吴秀清 2009 物理学报 58 1391］
[30] ］Wu D, Zhu S Q 2007 Phys. Lett. A 363 202
[31] ］Nie L R, Mei D C 2007 Chin. Phys. Lett. 24 3074
[32] ］Wang C J, Mei D C 2008 Mod. Phys. Lett. B 22 2677
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