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For an over-damped linear oscillator driven by multiplicative quadratic noise and periodic modulated noise, the exact analytical expressions of the first two moments, the amplitude and variance of the system steady-state response are obtained. We find that this system has richer dynamic behaviors than the traditional linear systems driven by linear noise; when the coefficients of the quadratic noise satisfy certain conditions, both the amplitude and the variance of the system steady-state response present stochastic resonance.
[1] Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A: Math. Gen. 14 L453
[2] [3] Ya J, Si N Y, Jia R L 2000 Phys. Rev. E 62 1869
[4] Xiao Q L, Shi Q Z 2003 Phys. Rev. E 67 021104
[5] [6] Gitterman M 2003 Phys. Rev. E 67 057103
[7] [8] Gitterman M 2005 Physical A 352 309
[9] [10] [11] Berdichevsky V, Gitterman M 1999 Phys. Rev. E 60 1494
[12] [13] Jing H L, Yin X H 2006 Phys. Rev. E 74 051115
[14] [15] Ning L J, Xu W 2009 Acta Phys. Sin. 58 2889 (in Chinese) [宁丽娟, 徐伟 2009 58 2889]
[16] Li D S, Li J H 2010 Commun. Theor. Phys. 53 298
[17] [18] Gitterman M 2004 Phys. Rev. E 69 041101
[19] [20] [21] Katrin L, Romi M, Astrid R 2009 Phys. Rev. E 79 051128
[22] Jin Y F, Hu H Y 2009 Acta Phys. Sin. 58 2895 (in Chinese) [靳艳飞, 胡海岩 2009 58 2895]
[23] [24] [25] Zhou Y R, Guo F, Jiang S Q 2008 Journal of University of Electronic Science and Technology of China 37 232 (in Chinese) [周玉荣, 郭锋, 蒋世奇 2008 电子科技大学学报 37 232]
[26] [27] Guo F, Zhou Y R, Jiang S Q, Gu T X 2006 Chin. Phys. Lett. 23 1705
[28] Jin Y F, Xu W, Li W 2005 Acta Phys. Sin. 54 2562 (in Chinese) [靳艳飞, 徐伟, 李伟 2005 54 2562]
[29] [30] [31] Murray S I, Marlan O S, Willis E J 1974 Laser Physics (Reading, Mass.: Addison-Wesley) p197
[32] Zhang L Y, Cao Li, Wu D J 2008 Commun. Theor. Phys. 49 1310
[33] [34] [35] Hector C, Fernando M, Enrique T 2006 Phys. Rev. E 74 022102
[36] [37] Shapiro V E, Loginov V M 1978 Physical A 91 563
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[1] Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A: Math. Gen. 14 L453
[2] [3] Ya J, Si N Y, Jia R L 2000 Phys. Rev. E 62 1869
[4] Xiao Q L, Shi Q Z 2003 Phys. Rev. E 67 021104
[5] [6] Gitterman M 2003 Phys. Rev. E 67 057103
[7] [8] Gitterman M 2005 Physical A 352 309
[9] [10] [11] Berdichevsky V, Gitterman M 1999 Phys. Rev. E 60 1494
[12] [13] Jing H L, Yin X H 2006 Phys. Rev. E 74 051115
[14] [15] Ning L J, Xu W 2009 Acta Phys. Sin. 58 2889 (in Chinese) [宁丽娟, 徐伟 2009 58 2889]
[16] Li D S, Li J H 2010 Commun. Theor. Phys. 53 298
[17] [18] Gitterman M 2004 Phys. Rev. E 69 041101
[19] [20] [21] Katrin L, Romi M, Astrid R 2009 Phys. Rev. E 79 051128
[22] Jin Y F, Hu H Y 2009 Acta Phys. Sin. 58 2895 (in Chinese) [靳艳飞, 胡海岩 2009 58 2895]
[23] [24] [25] Zhou Y R, Guo F, Jiang S Q 2008 Journal of University of Electronic Science and Technology of China 37 232 (in Chinese) [周玉荣, 郭锋, 蒋世奇 2008 电子科技大学学报 37 232]
[26] [27] Guo F, Zhou Y R, Jiang S Q, Gu T X 2006 Chin. Phys. Lett. 23 1705
[28] Jin Y F, Xu W, Li W 2005 Acta Phys. Sin. 54 2562 (in Chinese) [靳艳飞, 徐伟, 李伟 2005 54 2562]
[29] [30] [31] Murray S I, Marlan O S, Willis E J 1974 Laser Physics (Reading, Mass.: Addison-Wesley) p197
[32] Zhang L Y, Cao Li, Wu D J 2008 Commun. Theor. Phys. 49 1310
[33] [34] [35] Hector C, Fernando M, Enrique T 2006 Phys. Rev. E 74 022102
[36] [37] Shapiro V E, Loginov V M 1978 Physical A 91 563
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