乘性二次噪声驱动的线性过阻尼振子的随机共振

张路; 钟苏川; 彭皓; 罗懋康

doi:10.7498/aps.61.130503

摘要

针对乘性二次噪声和加性周期调制噪声联合驱动的线性过阻尼振子, 利用随机平均法推导了系统响应的一阶、二阶稳态矩以及稳态响应振幅和方差的解析表达式. 理论分析和仿真实验均表明这类系统具有比传统的由线性噪声驱动的线性系统更丰富的动力学特性; 当二次噪声的系数满足一定条件时, 系统稳态响应的振幅及方差均存在广义随机共振现象.

关键词:

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.

Keywords:

作者及机构信息

1.
四川大学数学学院, 成都 610065;

2.
电子信息控制重点实验室, 成都 610036

基金项目: 国家自然科学基金(批准号: 10731050)和教育部长江学者和创新团队发展计划(批准号: IRTO0742) 资助的课题.

Authors and contacts

1.
College of Mathematics, Sichuan University, Chengdu 610065, China;

2.
Science and Technology on Electronic Information Control Laboratory, Chengdu 610036, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 10731050), and the Program for Changjiang Scholars and Innovative Research Team in University of Ministry of Education of China (Grant No. IRTO0742).

参考文献

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[4]	Xiao Q L, Shi Q Z 2003 Phys. Rev. E 67 021104
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[27]	Guo F, Zhou Y R, Jiang S Q, Gu T X 2006 Chin. Phys. Lett. 23 1705
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施引文献

[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 物理学报 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 物理学报 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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