色噪声参激和周期调制噪声外激联合驱动的分数阶线性振子的共振行为

屠浙; 彭皓; 王飞; 马洪

doi:10.7498/aps.62.030502

摘要

研究了色噪声参激和周期调制噪声外激联合驱动的分数阶线性振子及其共振行为, 利用Laplace变换和Shapiro-Loginov公式, 推导出了系统响应的一阶矩及稳态响应振幅的解析表达式. 讨论了系统阶数、摩擦系数、周期驱动力频率、色噪声强度和相关率等参数对系统稳态响应的影响, 发现系统稳态响应振幅具有非单调变化的特点, 即出现了广义随机共振现象. 并且在适当参数下, 稳态响应振幅还存在具有双峰的广义随机共振现象.

关键词:

Abstract

The resonant behavior of a fractional linear oscillator subjected to both parametric excitation of colored noise and external excitation of periodically modulated noise is considered. Using Laplace transformation technique and Shapiro-Loginov formula, exact expressions of the first moment for the system response and its long-time amplitude are presented. The influence of the system parameters on the long-time behavior of the system response is discussed, such as fractional order, friction coefficient, driving frequency, noise intensity and relevant rate. It is found that the long-time amplitude of the fractional oscillator behaves non-monotonical, that is, there exist stochastic resonances in a wide sense. Moreover, generalized stochastic resonance with two peaks can be found subject to some appropriate parameters.

Keywords:

fractional linear oscillator /
periodically modulated noise /
stochastic resonance /
multi-peak generalized stochastic resonance

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: 11171238) 资助的课题.

Authors and contacts

1.
Department 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. 11171238).

参考文献

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[3]	McNamara B, Wiesenfeld K, Roy R 1988 Phys. Rev. Lett. 60 2626
[4]	Gang H, Nicolis G, Nicolis C 1990 Phys. Rev. A 42 2030
[5]	Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Science and Technology Education Press) (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)]
[6]	Gitterman M 2003 Phys. Rev. E 67 057103
[7]	Jia Y, Yu S N, Li J R 2000 Phys. Rev. E 62 1869
[8]	Berdichevsky V, Gitterman M 1996 Europhys. Lett. 36 161
[9]	Luo X, Zhu S 2003 Phys. Rev. E 67 021104
[10]	Berdichevsky V, Gitterman M 1999 Phys. Rev. E 60 1494
[11]	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]
[12]	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]
[13]	Qian M, Wang Y, Zhang X J 2003 Chin. Phys. Lett. 20 810
[14]	Liu F, Anh V, Turner I, Zhuang P 2003 J. Appl. Math. Comput. 13 233
[15]	Huang F, Liu F 2005 Anziam J. 46 317
[16]	Bao J D 2009 Stochastic Simulation Method of Classic and Quantum Dissipative Sysmtem (Beijing: Science Press) p160 (in Chinese) [包景东 2009 经典和量子耗散系统的随机模拟方法 (北京: 科学出版社) 第84页]
[17]	Zhou Y Q 2006 Stochastic Process Theory (2 Edn.) (Beijing: Publishing House of Electronics Industry) p94 (in Chinese) [周荫清 2006 随机过程理论 (第2版) (北京: 电子工业出版社) 第94页]
[18]	Shapiro V E, Loginov V M 1978 Physica A 91 563
[19]	Kempfle S, Schäfer I, Beyer H 2002 Nonlinear Dynam. 29 99
[20]	Laas K, Mankin R, Reiter E 2011 Int. J. Math. Mod. Meth. Appl. S 5 280
[21]	Soika E, Mankin R, Ainsaar A 2010 Phys. Rev. E 81 011141
[22]	Kubo R, Toda M, Hashitsume N 1985 Statistical Physics II (Berlin: Springer)
[23]	Sauga A, Mankin R, Ainsaar A 2010 WSEAS Transactions on Systems 18 21

施引文献

[1]	Benzi R, Sutera A, Vulpiana A 1981 J. Phys. A 14 L453
[2]	Gammaitoni L, Hänggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
[3]	McNamara B, Wiesenfeld K, Roy R 1988 Phys. Rev. Lett. 60 2626
[4]	Gang H, Nicolis G, Nicolis C 1990 Phys. Rev. A 42 2030
[5]	Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Science and Technology Education Press) (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)]
[6]	Gitterman M 2003 Phys. Rev. E 67 057103
[7]	Jia Y, Yu S N, Li J R 2000 Phys. Rev. E 62 1869
[8]	Berdichevsky V, Gitterman M 1996 Europhys. Lett. 36 161
[9]	Luo X, Zhu S 2003 Phys. Rev. E 67 021104
[10]	Berdichevsky V, Gitterman M 1999 Phys. Rev. E 60 1494
[11]	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]
[12]	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]
[13]	Qian M, Wang Y, Zhang X J 2003 Chin. Phys. Lett. 20 810
[14]	Liu F, Anh V, Turner I, Zhuang P 2003 J. Appl. Math. Comput. 13 233
[15]	Huang F, Liu F 2005 Anziam J. 46 317
[16]	Bao J D 2009 Stochastic Simulation Method of Classic and Quantum Dissipative Sysmtem (Beijing: Science Press) p160 (in Chinese) [包景东 2009 经典和量子耗散系统的随机模拟方法 (北京: 科学出版社) 第84页]
[17]	Zhou Y Q 2006 Stochastic Process Theory (2 Edn.) (Beijing: Publishing House of Electronics Industry) p94 (in Chinese) [周荫清 2006 随机过程理论 (第2版) (北京: 电子工业出版社) 第94页]
[18]	Shapiro V E, Loginov V M 1978 Physica A 91 563
[19]	Kempfle S, Schäfer I, Beyer H 2002 Nonlinear Dynam. 29 99
[20]	Laas K, Mankin R, Reiter E 2011 Int. J. Math. Mod. Meth. Appl. S 5 280
[21]	Soika E, Mankin R, Ainsaar A 2010 Phys. Rev. E 81 011141
[22]	Kubo R, Toda M, Hashitsume N 1985 Statistical Physics II (Berlin: Springer)
[23]	Sauga A, Mankin R, Ainsaar A 2010 WSEAS Transactions on Systems 18 21

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