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A class of nonlinear generalized Duffing equation for disturbed oscillator is considered. Firstly, the typical Duffing equation is solved. Then approximate solutions to the nonlinear Duffing equation for disturbed oscillators in stochastic resonance is obtained using the generalized functional variation principle, and the uniform validity is proved.
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Keywords:
- disturbed oscillator /
- resonance mechanism /
- asymptotic solution
[1] Benzi R, Sutera A, Vulpiana 1981 Physica A 14 453
[2] Bensi R, Parisi G, Srutera A 1982 Tellus 34 11
[3] [4] [5] Nicolis C 1982 Tellus 1 1
[6] Gammaitoni L, Hnggi P, Jung P, Marchesoni F 1998 Rew. Mod. Phys. 70 223
[7] [8] Gammaitoni L, Marchesoni F, Menichella-Saetta E, Santucci S 1989 Phys. Rev. Lett. 62 349
[9] [10] Gammaitoni L, Menichella-Saetta E, Santucci S, Marchesoni F, Presilla C 1989 Phys. Rev. A 40 2114
[11] [12] [13] Jung P, Hnggi P 1990 Phys. Rev. A 41 2977
[14] Kang Y M, Xu J X, Xie Y 2003 Acta Phys. Sin. 52 802 (in Chinese)[康艳梅, 徐健学, 谢勇 2003 52 802]
[15] [16] [17] Wang F Z, Chen W S, Qin G R, Guo D Y, Liu J L 2003 Chin. Phys. Lett. 20 27
[18] Leng Y G, Lai Z H, Fan S B, Gao Y J 2012 Acta Phys. Sin. 61 230502 (in Chinese)[冷永刚, 赖志慧, 范胜波, 高毓璣 2012 61 230502]
[19] [20] Leng Y G, Lai Z H 2014 Acta Phys. Sin. 63 020502(in Chinese)[冷永刚, 赖志慧 2014 63 020502]
[21] [22] Han X L, Shi L F, Mo J Q 2014 Acta Phys. Sin. 63 060205 (in Chinese)[韩祥临, 石兰芳, 莫嘉琪 2014 63 060205]
[23] [24] Han X L, Zhao Z J, Cheng R J, Mo J Q 2013 Acta Phys. Sin. 62 110202 (in Chinese)[韩祥临, 赵振江, 程荣军, 莫嘉琪 2013 62 110202]
[25] [26] [27] Yao J S, Lin W T, Du Z J, Mo J Q 2012 Chin. Phys. B 21 120205
[28] [29] Lin W T, Zhang Y, Mo J Q 2013 Chin. Phys. B 22 030205
[30] [31] Ouyang C, Chen L H, Mo J Q 2012 Chin. Phys. B 21 050203
[32] Zhou X C, Yao J S, Mo J Q 2012 Chin. Phys. B 21 030201
[33] [34] Zhou X C, Shi L F, Mo J Q 2014 Chin. Phys. B 23 040202
[35] [36] Mo J Q, Lin W T, Lin Y H 2011 Chin. Phys. B 20 010208
[37] [38] [39] Mo J Q 2009 Chin. Phys. Lett. 26 010241
[40] [41] Lin W T, Zhang Y, Mo J Q 2013 Chin. Phys. B 22 030205
[42] [43] He J H 2002 Approximate Analytical Methods in Engineering and Sciences (Zhengzhou: Henan Science and Technology Publisher) (in Chinese)[何吉欢 2002 工程和科学中的近似非线性分析方法 (郑州: 河南科学技术出版社)])
[44] de Jager, E. M, Jiang Furu 1996 The Theory of Singular Perturbation, Amsterdam: North-Holland Publishing Co
[45] -
[1] Benzi R, Sutera A, Vulpiana 1981 Physica A 14 453
[2] Bensi R, Parisi G, Srutera A 1982 Tellus 34 11
[3] [4] [5] Nicolis C 1982 Tellus 1 1
[6] Gammaitoni L, Hnggi P, Jung P, Marchesoni F 1998 Rew. Mod. Phys. 70 223
[7] [8] Gammaitoni L, Marchesoni F, Menichella-Saetta E, Santucci S 1989 Phys. Rev. Lett. 62 349
[9] [10] Gammaitoni L, Menichella-Saetta E, Santucci S, Marchesoni F, Presilla C 1989 Phys. Rev. A 40 2114
[11] [12] [13] Jung P, Hnggi P 1990 Phys. Rev. A 41 2977
[14] Kang Y M, Xu J X, Xie Y 2003 Acta Phys. Sin. 52 802 (in Chinese)[康艳梅, 徐健学, 谢勇 2003 52 802]
[15] [16] [17] Wang F Z, Chen W S, Qin G R, Guo D Y, Liu J L 2003 Chin. Phys. Lett. 20 27
[18] Leng Y G, Lai Z H, Fan S B, Gao Y J 2012 Acta Phys. Sin. 61 230502 (in Chinese)[冷永刚, 赖志慧, 范胜波, 高毓璣 2012 61 230502]
[19] [20] Leng Y G, Lai Z H 2014 Acta Phys. Sin. 63 020502(in Chinese)[冷永刚, 赖志慧 2014 63 020502]
[21] [22] Han X L, Shi L F, Mo J Q 2014 Acta Phys. Sin. 63 060205 (in Chinese)[韩祥临, 石兰芳, 莫嘉琪 2014 63 060205]
[23] [24] Han X L, Zhao Z J, Cheng R J, Mo J Q 2013 Acta Phys. Sin. 62 110202 (in Chinese)[韩祥临, 赵振江, 程荣军, 莫嘉琪 2013 62 110202]
[25] [26] [27] Yao J S, Lin W T, Du Z J, Mo J Q 2012 Chin. Phys. B 21 120205
[28] [29] Lin W T, Zhang Y, Mo J Q 2013 Chin. Phys. B 22 030205
[30] [31] Ouyang C, Chen L H, Mo J Q 2012 Chin. Phys. B 21 050203
[32] Zhou X C, Yao J S, Mo J Q 2012 Chin. Phys. B 21 030201
[33] [34] Zhou X C, Shi L F, Mo J Q 2014 Chin. Phys. B 23 040202
[35] [36] Mo J Q, Lin W T, Lin Y H 2011 Chin. Phys. B 20 010208
[37] [38] [39] Mo J Q 2009 Chin. Phys. Lett. 26 010241
[40] [41] Lin W T, Zhang Y, Mo J Q 2013 Chin. Phys. B 22 030205
[42] [43] He J H 2002 Approximate Analytical Methods in Engineering and Sciences (Zhengzhou: Henan Science and Technology Publisher) (in Chinese)[何吉欢 2002 工程和科学中的近似非线性分析方法 (郑州: 河南科学技术出版社)])
[44] de Jager, E. M, Jiang Furu 1996 The Theory of Singular Perturbation, Amsterdam: North-Holland Publishing Co
[45]
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