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According to the exited stochastic resonance theory, we cannot obtain the dynamic behavior of a stochastic resonance (SR) system intuitively. In order to reveal the dynamic mechanism of SR, a kind of first-order Duffing equation attractor is analyzed at first, and then the property of nonlinear Duffing equation is studied, based on which the nonautonomous Duffing equation attractor curve is deduced. The output of SR system can be obtained by mapping the input signal on the attractor curve, and the dynamic mechanism of SR is explained by using the mapping method. Analysis of the result indicates that the intrinsic signal can push the system to move along the attractor curve, and the noise can evoke a transition response of the system under the given conditions. Some exited SR weak signal detection methods, such as the parameter-adjustment and damping-adjustment are extended by the proposed dynamic mechanism.
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Keywords:
- stochastic resonance /
- weak signal detection /
- attractor curve
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[2] Hu G, Qing G R, Gong D C 1991 Phys. Rev. A 44 6414
[3] McNamara B, Wiesenfeld K 1989 Phys. Rev. A 39 4854
[4] Dykman M I 1990 Phys. Rev. Lett. 65 2606
[5] Gammaitoni L, Marchesoni F 1989 Phys. Rev. Lett. 62 349
[6] Dykman M I, Haken H, Hu G 1993 Phys. Lett. A 180 332
[7] Dykman M I, Luchinsky D G, Mannella R 1994 Phys. Lett. A 193 61
[8] Zhou T, Moss F 1990 Phys. Rev. A 41 4255
[9] Choi M H, Fox R F, Jung P 1998 Phys. Rev. E 57 6335
[10] Giacomelli G, Marin F, Rabbiosi I 1999 Phys. Rev. Lett. 82 675
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[12] Hu G, Nicolis G, Nicolis C 1990 Phys. Rev. A 42 2030
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[14] Li X L, Leng Y G, Fan S B, Shi P 2011 J. Vibration and Shock. 30 78 (in Chinese) [李晓龙, 冷永刚, 范胜波, 石鹏 2011 振动与冲击 30 78]
[15] Peng H, Zhong S C, Ma H 2013 Acta Phys. Sin. 62 080501 (in Chinese)[彭皓, 钟苏川, 马洪 2013 62 080501]
[16] Guo F, Luo X D, Li S F, Zhou Y R 2010 Chin. Phys. B 19 080502
[17] Lin M, Fang L M, Zheng Y J 2009 Chin. Phys. B 18 1725
[18] Li J L, Zeng L Z 2011 Chin. Phys. B 20 010503
[19] Zhang L Y, Jin G X, Cao L, Wang Z Y 2012 Chin. Phys. B 21 120502
[20] Jiang S Q, Hou M J, Jia C H, He J R, Gu T X 2009 Chin. Phys. B 18 2667
[21] Leng Y G, Wang T Y, Guo Y 2007 Acta Phys. Sin. 56 30 (in Chinese)[冷永刚, 王太勇, 郭焱 2007 56 30]
[22] Leng Y G 2011 Acta Phys. Sin. 60 020503 (in Chinese)[冷永刚 2011 60 020503]
[23] Wang G F, Ouyang S, Zhang H R 2010 J. Guilin Univ. Elec. Tec. 30 396 (in Chinese) [王国富, 欧阳缮, 张海如 2010 桂林电子科技大学学报 30 396]
[24] Qu Y, Wang F Z, Sun J J 2011 Sci. sin. 41 1190 (in Chinese) [曲媛, 王辅忠, 孙静静 2011 中国科学 41 1190]
[25] Zhao W L, Wang J, Wang L Z 2013 Chaos 23 033117
[26] Fan Y Y, Li L P, Dang R R 2013 Chin. J. Scie. Ins. 34 566 (in Chinese) [樊养余, 李利品, 党瑞荣 2013 仪器仪表学报 34 566]
[27] Zhao W L, Liu J, Yin Y P 2011 Chin. J. Scie. Ins. 32 721 (in Chinese) [赵文礼, 刘进, 殷园平 2011 仪器仪表学报 32 721]
[28] Leng Y G, Wang T Y 2003 Acta Phys. Sin. 52 2431 (in Chinese)[冷永刚, 王太勇 2003 52 2431]
[29] Wang L Z, Zhao W L, Chen X 2012 Acta Phys. Sin. 61 160501 (in Chinese)[王林泽, 赵文礼, 陈旋 2012 61 160501]
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[1] Benzi R, Parisi G, Sutera A, Vulpiana A 1981 J. Phys. A: Math. Gen. 14 453
[2] Hu G, Qing G R, Gong D C 1991 Phys. Rev. A 44 6414
[3] McNamara B, Wiesenfeld K 1989 Phys. Rev. A 39 4854
[4] Dykman M I 1990 Phys. Rev. Lett. 65 2606
[5] Gammaitoni L, Marchesoni F 1989 Phys. Rev. Lett. 62 349
[6] Dykman M I, Haken H, Hu G 1993 Phys. Lett. A 180 332
[7] Dykman M I, Luchinsky D G, Mannella R 1994 Phys. Lett. A 193 61
[8] Zhou T, Moss F 1990 Phys. Rev. A 41 4255
[9] Choi M H, Fox R F, Jung P 1998 Phys. Rev. E 57 6335
[10] Giacomelli G, Marin F, Rabbiosi I 1999 Phys. Rev. Lett. 82 675
[11] Jung P, P Hänggi 1989 Euro. phys. Lett. 8 505
[12] Hu G, Nicolis G, Nicolis C 1990 Phys. Rev. A 42 2030
[13] Lu Z H, Lin J H, Hu G 1993 Acta Phys. Sin. 42 1556 (in Chinese)[卢志恒, 林建恒, 胡岗 1993 42 1556]
[14] Li X L, Leng Y G, Fan S B, Shi P 2011 J. Vibration and Shock. 30 78 (in Chinese) [李晓龙, 冷永刚, 范胜波, 石鹏 2011 振动与冲击 30 78]
[15] Peng H, Zhong S C, Ma H 2013 Acta Phys. Sin. 62 080501 (in Chinese)[彭皓, 钟苏川, 马洪 2013 62 080501]
[16] Guo F, Luo X D, Li S F, Zhou Y R 2010 Chin. Phys. B 19 080502
[17] Lin M, Fang L M, Zheng Y J 2009 Chin. Phys. B 18 1725
[18] Li J L, Zeng L Z 2011 Chin. Phys. B 20 010503
[19] Zhang L Y, Jin G X, Cao L, Wang Z Y 2012 Chin. Phys. B 21 120502
[20] Jiang S Q, Hou M J, Jia C H, He J R, Gu T X 2009 Chin. Phys. B 18 2667
[21] Leng Y G, Wang T Y, Guo Y 2007 Acta Phys. Sin. 56 30 (in Chinese)[冷永刚, 王太勇, 郭焱 2007 56 30]
[22] Leng Y G 2011 Acta Phys. Sin. 60 020503 (in Chinese)[冷永刚 2011 60 020503]
[23] Wang G F, Ouyang S, Zhang H R 2010 J. Guilin Univ. Elec. Tec. 30 396 (in Chinese) [王国富, 欧阳缮, 张海如 2010 桂林电子科技大学学报 30 396]
[24] Qu Y, Wang F Z, Sun J J 2011 Sci. sin. 41 1190 (in Chinese) [曲媛, 王辅忠, 孙静静 2011 中国科学 41 1190]
[25] Zhao W L, Wang J, Wang L Z 2013 Chaos 23 033117
[26] Fan Y Y, Li L P, Dang R R 2013 Chin. J. Scie. Ins. 34 566 (in Chinese) [樊养余, 李利品, 党瑞荣 2013 仪器仪表学报 34 566]
[27] Zhao W L, Liu J, Yin Y P 2011 Chin. J. Scie. Ins. 32 721 (in Chinese) [赵文礼, 刘进, 殷园平 2011 仪器仪表学报 32 721]
[28] Leng Y G, Wang T Y 2003 Acta Phys. Sin. 52 2431 (in Chinese)[冷永刚, 王太勇 2003 52 2431]
[29] Wang L Z, Zhao W L, Chen X 2012 Acta Phys. Sin. 61 160501 (in Chinese)[王林泽, 赵文礼, 陈旋 2012 61 160501]
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