搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

带反馈的分数阶耦合布朗马达的定向输运

秦天奇 王飞 杨博 罗懋康

引用本文:
Citation:

带反馈的分数阶耦合布朗马达的定向输运

秦天奇, 王飞, 杨博, 罗懋康

Transport properties of fractional coupled Brownian motors in ratchet potential with feedback

Qin Tian-Qi, Wang Fei, Yang Bo, Luo Mao-Kang
PDF
导出引用
  • 研究具有幂律记忆性的带反馈耦合布朗马达的定向输运现象, 引入分数阶理论, 建立了带反馈的分数阶耦合布朗马达模型, 利用分数阶差分法求得模型数值解并分析了模型参数对合作定向输运性质的影响. 仿真结果表明, 系统的记忆性通过影响带反馈的棘齿势的打开和闭合而影响粒子的定向输运, 即当系统的阶数在较小的范围内, 系统的记忆性会使带反馈的棘齿势的开关频率增加, 从而增大定向流速; 当系统其他参数(势垒高度、噪声强度等)固定时, 输运速度随着阶数的变化出现广义随机共振现象.
    Based on the theory of fractional integration, direct transport behaviors of coupled Brownian motors with feedback control in viscoelastic media are investigated. The mathematical model of fractional overdamped coupled Brownian motors is established by adopting the power function as damping kernel function of general Langevin equation due to the power-law memory characteristics of cytosol in biological cells. Numerical solution is observed by fractional difference method and the influence of model parameters on cooperative direct transport of the coupled Brownian motors is discussed in detail by numerical simulation. The research shows that the memory of the fractional dynamical system can affect the direct transport phenomenon of the coupled Brownian motors through changing the on-off switching frequency of the ratchet potential with feedback control. To be more specific, in a proper range of the fractional order, the memory of the dynamical system can increase the on-off switching frequency of the ratchet potential, which can lead to the velocity increase of the direct transport. Furthermore, in the case of small fractional order, since the coupled Brownian motors move under the competition between the damping force with memory and the potential force with feedback control, the resultant force exerted on the coupled particles is always positive when the ratchet potential with feedback control is on although the fractional damping force is large, which leads to the result that the coupled Brownian motors move in the positive direction in the mass. On the contrary, in the case of large fractional order, the on-off switching frequency of potential with feedback control becomes small, as a result of which the main influential factor of the direct transport becomes the potential depth. Therefore the coupled Brownian motors are more likely to stay in the potential wells for a long time because the probability that describes the possibility that the coupled Brownian motors surmount the potential barriers becomes small. Finally, with the parameters of the fractional dynamical system (e.g. potential depth, noise intensity) fixed, the direct transport velocity of the coupled Brownian motors shows the generalized stochastic resonant phenomenon while the fractional order varies.
    • 基金项目: 国家自然科学基金(批准号:11171238)和电子信息控制重点实验室基金(批准号:2013035)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grand No. 11171238) and the Foundation of Science and Technology on Electronic Information Control Laboratory, China (Grant No. 2013035).
    [1]

    Nishyama M, Muto E, Inoue Y, Yanagida T, Higuchi H 2001 Nature Cell Biology 3 425

    [2]

    Reimann P 2002 Phys. Rep. 361 57

    [3]

    Cordova N G, Ermentrout B, Oster G 1992 Proc. Natl. Acad. Sci. USA 89 339

    [4]

    Gao T F, Zhang Y, Chen J C 2009 Chin. Phys. B 18 3279

    [5]

    Zeng C H, Wang H 2012 Chin. Phys. B 21 050502

    [6]

    Ai B Q, He Y F, Zhong W R 2011 Phys. Rev. E 83 051106

    [7]

    Dan D, Jayannavarar A M, Menon G I 2003 Physica A 318 40

    [8]

    Rozenbaum V M, Yang D Y, Lin S H, Tsong T Y 2006 Physica A 363 211

    [9]

    Dinis L, Parron do J M R, Cao F J 2005 Europhys. Lett. 71 536

    [10]

    Lindén M, Tuohimaa T, Jonsson A B, Wallin M F 2006 Phys. Rev. E 74 021908

    [11]

    Craig E M, Zuckermann M J, Linke H J 2006 Phys. Rev. E 73 051106

    [12]

    Lattanzi G, Maritan A 2001 Phys. Rev. Lett. 86 1134

    [13]

    Cao F J, Dinis L, Parrondo J M R 2004 Phys. Rev. Lett. 93 040603

    [14]

    Feito M, Cao F J 2006 Phys. Rev. E 74 041109

    [15]

    Feito M, Cao F J 2007 Eur. Phys. J. B 59 63

    [16]

    Feito M, Cao F J 2007 Phys. Rev. E 76 061113

    [17]

    Feito M, Cao F J 2008 Physica A 387 4553

    [18]

    Gao T F, Chen J C 2009 J. Phys. A: Math. Theor. 42 065002

    [19]

    Zhao A K, Zhang H W, Li Y X 2010 Chin. Phys. B 19 110506

    [20]

    Wang L F, Gao T F, Huang R Z, Zheng Y X 2013 Acta Phys. Sin. 62 070502 (in Chinese) [王莉芳, 高天附, 黄仁忠, 郑玉祥 2013 物理学报 62 070502]

    [21]

    Evstigneev M, Gehlen S, Reimann P 2009

    [22]

    Gao T F, Liu F S, Chen J C 2012 Chin. Phys. B 21 020502

    [23]

    Bier M 2007 Biosystems 88 301

    [24]

    Zhang H W, Wen S T, Chen G R, Li Y X, Cao Z X, Li W 2012 Chin. Phys. B 21 038701

    [25]

    Bustamante C, Chemla Y R, Forde N R, Izhaky D 2004 Annu. Rev. Biochem. 73 705

    [26]

    Cao F J, Feito M, Touchette H 2009 Physica A 388 113

    [27]

    Mathur A B, Collinsworth A M, Reichert W M, Kraus W E, Truskey G A 2001 J. Biomech. 34 1545

    [28]

    Azuma N, Aysin S D, Ikeda M, Kito H, Akadaka N, Sasajima T, Sumpio B E 2000 J. Vasc. Surg. 32 789

    [29]

    Guilak F, Tedrow J R, Burgkart R 2000 Biochem. Biophys. Res. Commun. 269 781

    [30]

    Bao J D 2012 Introduction to Anomalous Statistics Dynamics (Beijing: Science Press) p196 (in Chinese) [包景东 2012 反常统计动力学导论 (北京: 科学出版社) 第196页]

    [31]

    Widom A 1971 Phys. Rev. A 3 1394

    [32]

    Lin L F, Zhou X W, Ma H 2013 Acta Phys. Sin. 62 240501 (in Chinese) [林丽烽, 周兴旺, 马洪 2013 物理学报 62 240501]

    [33]

    Bai W S M, Peng H, Tu Z, Ma H 2012 Acta Phys. Sin. 61 210501 (in Chinese) [白文斯密, 彭皓, 屠浙, 马洪 2012 物理学报 61 210501]

    [34]

    Gitterman M 2005 Phys. Stat. Mech. Appl. 352 309

    [35]

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

    [36]

    Liu F, Anh V, Turner I, Zhuang P 2003 J. Appl. Math. Comput. 13 233

    [37]

    Petrás I 2011 Fractional-Order Nonlinear Systerms Modeling, Analysis and Simulation (1st Ed.) (Beijing: Higher Education Press) p19

  • [1]

    Nishyama M, Muto E, Inoue Y, Yanagida T, Higuchi H 2001 Nature Cell Biology 3 425

    [2]

    Reimann P 2002 Phys. Rep. 361 57

    [3]

    Cordova N G, Ermentrout B, Oster G 1992 Proc. Natl. Acad. Sci. USA 89 339

    [4]

    Gao T F, Zhang Y, Chen J C 2009 Chin. Phys. B 18 3279

    [5]

    Zeng C H, Wang H 2012 Chin. Phys. B 21 050502

    [6]

    Ai B Q, He Y F, Zhong W R 2011 Phys. Rev. E 83 051106

    [7]

    Dan D, Jayannavarar A M, Menon G I 2003 Physica A 318 40

    [8]

    Rozenbaum V M, Yang D Y, Lin S H, Tsong T Y 2006 Physica A 363 211

    [9]

    Dinis L, Parron do J M R, Cao F J 2005 Europhys. Lett. 71 536

    [10]

    Lindén M, Tuohimaa T, Jonsson A B, Wallin M F 2006 Phys. Rev. E 74 021908

    [11]

    Craig E M, Zuckermann M J, Linke H J 2006 Phys. Rev. E 73 051106

    [12]

    Lattanzi G, Maritan A 2001 Phys. Rev. Lett. 86 1134

    [13]

    Cao F J, Dinis L, Parrondo J M R 2004 Phys. Rev. Lett. 93 040603

    [14]

    Feito M, Cao F J 2006 Phys. Rev. E 74 041109

    [15]

    Feito M, Cao F J 2007 Eur. Phys. J. B 59 63

    [16]

    Feito M, Cao F J 2007 Phys. Rev. E 76 061113

    [17]

    Feito M, Cao F J 2008 Physica A 387 4553

    [18]

    Gao T F, Chen J C 2009 J. Phys. A: Math. Theor. 42 065002

    [19]

    Zhao A K, Zhang H W, Li Y X 2010 Chin. Phys. B 19 110506

    [20]

    Wang L F, Gao T F, Huang R Z, Zheng Y X 2013 Acta Phys. Sin. 62 070502 (in Chinese) [王莉芳, 高天附, 黄仁忠, 郑玉祥 2013 物理学报 62 070502]

    [21]

    Evstigneev M, Gehlen S, Reimann P 2009

    [22]

    Gao T F, Liu F S, Chen J C 2012 Chin. Phys. B 21 020502

    [23]

    Bier M 2007 Biosystems 88 301

    [24]

    Zhang H W, Wen S T, Chen G R, Li Y X, Cao Z X, Li W 2012 Chin. Phys. B 21 038701

    [25]

    Bustamante C, Chemla Y R, Forde N R, Izhaky D 2004 Annu. Rev. Biochem. 73 705

    [26]

    Cao F J, Feito M, Touchette H 2009 Physica A 388 113

    [27]

    Mathur A B, Collinsworth A M, Reichert W M, Kraus W E, Truskey G A 2001 J. Biomech. 34 1545

    [28]

    Azuma N, Aysin S D, Ikeda M, Kito H, Akadaka N, Sasajima T, Sumpio B E 2000 J. Vasc. Surg. 32 789

    [29]

    Guilak F, Tedrow J R, Burgkart R 2000 Biochem. Biophys. Res. Commun. 269 781

    [30]

    Bao J D 2012 Introduction to Anomalous Statistics Dynamics (Beijing: Science Press) p196 (in Chinese) [包景东 2012 反常统计动力学导论 (北京: 科学出版社) 第196页]

    [31]

    Widom A 1971 Phys. Rev. A 3 1394

    [32]

    Lin L F, Zhou X W, Ma H 2013 Acta Phys. Sin. 62 240501 (in Chinese) [林丽烽, 周兴旺, 马洪 2013 物理学报 62 240501]

    [33]

    Bai W S M, Peng H, Tu Z, Ma H 2012 Acta Phys. Sin. 61 210501 (in Chinese) [白文斯密, 彭皓, 屠浙, 马洪 2012 物理学报 61 210501]

    [34]

    Gitterman M 2005 Phys. Stat. Mech. Appl. 352 309

    [35]

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

    [36]

    Liu F, Anh V, Turner I, Zhuang P 2003 J. Appl. Math. Comput. 13 233

    [37]

    Petrás I 2011 Fractional-Order Nonlinear Systerms Modeling, Analysis and Simulation (1st Ed.) (Beijing: Higher Education Press) p19

  • [1] 刘天宇, 曹佳慧, 刘艳艳, 高天附, 郑志刚. 温度反馈控制棘轮的最优控制. 物理学报, 2021, 70(19): 190501. doi: 10.7498/aps.70.20210517
    [2] 范黎明, 吕明涛, 黄仁忠, 高天附, 郑志刚. 反馈控制棘轮的定向输运效率研究. 物理学报, 2017, 66(1): 010501. doi: 10.7498/aps.66.010501
    [3] 谢天婷, 邓科, 罗懋康. 二维非对称周期时移波状通道中的粒子定向输运问题. 物理学报, 2016, 65(15): 150501. doi: 10.7498/aps.65.150501
    [4] 吴魏霞, 宋艳丽, 韩英荣. 二维耦合定向输运模型研究. 物理学报, 2015, 64(15): 150501. doi: 10.7498/aps.64.150501
    [5] 杨建强, 马洪, 钟苏川. 分数阶对数耦合系统在非周期外力作用下的定向输运现象. 物理学报, 2015, 64(17): 170501. doi: 10.7498/aps.64.170501
    [6] 任芮彬, 刘德浩, 王传毅, 罗懋康. 时间非对称外力驱动分数阶布朗马达的定向输运. 物理学报, 2015, 64(9): 090505. doi: 10.7498/aps.64.090505
    [7] 周兴旺, 林丽烽, 马洪, 罗懋康. 时间非对称分数阶类Langevin棘齿. 物理学报, 2014, 63(11): 110501. doi: 10.7498/aps.63.110501
    [8] 王飞, 谢天婷, 邓翠, 罗懋康. 系统非对称性及记忆性对布朗马达输运行为的影响. 物理学报, 2014, 63(16): 160502. doi: 10.7498/aps.63.160502
    [9] 屠浙, 赖莉, 罗懋康. 分数阶非对称耦合系统在对称周期势中的定向输运. 物理学报, 2014, 63(12): 120503. doi: 10.7498/aps.63.120503
    [10] 曾喆昭. 不确定混沌系统的径向基函数神经网络反馈补偿控制. 物理学报, 2013, 62(3): 030504. doi: 10.7498/aps.62.030504
    [11] 吴魏霞, 郑志刚. 二维势场中弹性耦合粒子的定向输运研究. 物理学报, 2013, 62(19): 190511. doi: 10.7498/aps.62.190511
    [12] 林丽烽, 周兴旺, 马洪. 分数阶双头分子马达的欠扩散输运现象. 物理学报, 2013, 62(24): 240501. doi: 10.7498/aps.62.240501
    [13] 赖莉, 周薛雪, 马洪, 罗懋康. 分数阶布朗马达在闪烁棘齿势中的合作输运现象. 物理学报, 2013, 62(15): 150502. doi: 10.7498/aps.62.150502
    [14] 白文斯密, 彭皓, 屠浙, 马洪. 分数阶Brown马达及其定向输运现象. 物理学报, 2012, 61(21): 210501. doi: 10.7498/aps.61.210501
    [15] 黄丽莲, 辛方, 王霖郁. 新分数阶超混沌系统的研究与控制及其电路实现. 物理学报, 2011, 60(1): 010505. doi: 10.7498/aps.60.010505
    [16] 史正平. 简易混沌振荡器的混沌特性及其反馈控制电路的设计. 物理学报, 2010, 59(9): 5940-5948. doi: 10.7498/aps.59.5940
    [17] 林 敏, 黄咏梅, 方利民. 双稳系统随机共振的反馈控制. 物理学报, 2008, 57(4): 2041-2047. doi: 10.7498/aps.57.2041
    [18] 都 琳, 徐 伟, 贾飞蕾, 李 爽. 基于低通滤波函数实现陀螺系统的反馈控制. 物理学报, 2007, 56(7): 3813-3819. doi: 10.7498/aps.56.3813
    [19] 陈 漩, 高自友, 赵小梅, 贾 斌. 反馈控制双车道跟驰模型研究. 物理学报, 2007, 56(4): 2024-2029. doi: 10.7498/aps.56.2024
    [20] 刘素华, 唐驾时. Langford系统Hopf分叉的线性反馈控制. 物理学报, 2007, 56(6): 3145-3151. doi: 10.7498/aps.56.3145
计量
  • 文章访问数:  3242
  • PDF下载量:  231
  • 被引次数: 0
出版历程
  • 收稿日期:  2014-12-22
  • 修回日期:  2015-01-25
  • 刊出日期:  2015-06-05

带反馈的分数阶耦合布朗马达的定向输运

  • 1. 四川大学数学学院, 成都 610065
    基金项目: 国家自然科学基金(批准号:11171238)和电子信息控制重点实验室基金(批准号:2013035)资助的课题.

摘要: 研究具有幂律记忆性的带反馈耦合布朗马达的定向输运现象, 引入分数阶理论, 建立了带反馈的分数阶耦合布朗马达模型, 利用分数阶差分法求得模型数值解并分析了模型参数对合作定向输运性质的影响. 仿真结果表明, 系统的记忆性通过影响带反馈的棘齿势的打开和闭合而影响粒子的定向输运, 即当系统的阶数在较小的范围内, 系统的记忆性会使带反馈的棘齿势的开关频率增加, 从而增大定向流速; 当系统其他参数(势垒高度、噪声强度等)固定时, 输运速度随着阶数的变化出现广义随机共振现象.

English Abstract

参考文献 (37)

目录

    /

    返回文章
    返回