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过阻尼分数阶Langevin方程及其随机共振

高仕龙 钟苏川 韦鹍 马洪

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过阻尼分数阶Langevin方程及其随机共振

高仕龙, 钟苏川, 韦鹍, 马洪

Overdamped fractional Langevin equation and its stochastic resonance

Gao Shi-Long, Zhong Su-Chuan, Wei Kun, Ma Hong
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  • 通过对广义Langevin方程阻尼核函数的适当选取,在过阻尼的情形下, 推导出分数阶Langevin方程.给合反常扩散理论和分数阶导数的记忆性, 讨论了分数阶Langevin方程的物理意义,进而得出分数阶Langevin方程产生随机共振的内在机理.数值模拟表明,在一定的阶数范围内,分数阶Langevin方程可以产生随机共振, 并且分数阶下的信噪比增益好于整数阶情形.
    By choosing an appropriate damping kernel function of generalized Langevin equation, fractional Langevin equation (FLE) is derived in the case of overdamped condition. With the theory of anomalous diffusion and the memory of fractional derivatives, the physical meaning of FLE is discussed. Moreover, the internal mechanism of stochastic resonance about FLE is obtained. Finally, the numerical simulation shows that in a certain range of the order, stochastic resonance appears in FLE, and it is evident that the SNR gain in fractional Langevin equation is better than that of the integer-order situation.
    • 基金项目: 国家自然科学基金重点项目(批准号: 10731050)和中国博士后科学基金 (批准号: 20100471651, 201104693)资助的课题.
    • Funds: Project supported by the Key Program of the National Natural Science Foundation of China (Grant No. 10731050) and the China Postdoctoral Science Foundation (Grant No. 20100471651, 201104693).
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    Huang F, Liu F 2005 The ANZIAM J. 46 317

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    Wheatcraft S W, Benson D A, Meerschaert M M 2000 Water Resour. Res. 36 1403

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    De Andrade M F, Lenzi E K, Evangelista L R, Mendes R S, Malacarne L C 2005 Phys. Lett. A 347 160

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    Kenkre V M, Kus M, Dunlap D H, Parris P E 1998 Phys. Rev. E 58 99

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    Dong X J 2009 Chin. Phys. B 18 70

    [13]

    Zhang X Y, Xu W, Zhou B C 2011 Acta Phys. Sin. 60 060514 (in Chinese) [张晓燕, 徐伟, 周丙常 2011 物理学报 60 060514]

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    [17]

    Kou S C, X Sunney X 2004 Phys. Rev. Lett. 93 180603

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    Kou S C 2008 Ann. Appl. Statistics 2 501

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    [20]

    Ahmed E, Elgazzar A S 2007 Physica A 379 607

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  • [1]

    Bao J D 2009 Random Simulation Method of Classical and Quantum Dissipation System (Beijing: Science Press) p80 (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80页]

    [2]

    Deng W H, Barkai E 2009 Phys. Rev. E 79 011112

    [3]

    Benzi R, Sutera A, Vulpiana A 1981 J. Phys. A 14 L453

    [4]

    Lin M, Fang L M 2009 Acta Phys. Sin. 58 2136 (in Chinese) [林敏, 方利民 2009 物理学报 58 2136]

    [5]

    Yang J H, Liu X B 2010 Chin. Phys. B 19 050504

    [6]

    Gammaitoni L, Hanggi P, Jung P, Marchesoni F 1998 Rev. Modern Phys. 70 223

    [7]

    Huang F, Liu F 2005 The ANZIAM J. 46 317

    [8]

    Liu F, Turner I, Anh V 2003 J. Appl. Math. Comp. 13 233

    [9]

    Wheatcraft S W, Benson D A, Meerschaert M M 2000 Water Resour. Res. 36 1403

    [10]

    De Andrade M F, Lenzi E K, Evangelista L R, Mendes R S, Malacarne L C 2005 Phys. Lett. A 347 160

    [11]

    Kenkre V M, Kus M, Dunlap D H, Parris P E 1998 Phys. Rev. E 58 99

    [12]

    Dong X J 2009 Chin. Phys. B 18 70

    [13]

    Zhang X Y, Xu W, Zhou B C 2011 Acta Phys. Sin. 60 060514 (in Chinese) [张晓燕, 徐伟, 周丙常 2011 物理学报 60 060514]

    [14]

    Podlubny I 1999 Fractional Differential Equations (San Diegop, CA: Academic Press)

    [15]

    Samko S G, Kilbas A A, Marichev O I 1993 Marichev, Fractional Integrals and Derivatives Theory and Applications (New York, Gordon and Breach Science Publ.)

    [16]

    Oldham K B, Spanier J 1974 The Fractional Calculus (New York: Academic Press)

    [17]

    Kou S C, X Sunney X 2004 Phys. Rev. Lett. 93 180603

    [18]

    Kou S C 2008 Ann. Appl. Statistics 2 501

    [19]

    Hill T 1986 An Introduction to Statistical Thermodynamics (New York: Dover)

    [20]

    Ahmed E, Elgazzar A S 2007 Physica A 379 607

    [21]

    Tarasov V E 2009 J. Phys. A: Math. Theor. 42 465102

    [22]

    Tarasov V E 2009 J. Math. Phys. 50 122703

    [23]

    Goychuk I, Hanggi P 2003 Phys. Rev. Lett. 91 70601

    [24]

    Fauve S, Hesolt F 1983 Phys. Lett. A 97 5

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出版历程
  • 收稿日期:  2011-08-11
  • 修回日期:  2012-05-28
  • 刊出日期:  2012-05-05

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