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分数阶FitzHugh-Nagumo模型神经元的动力学特性及其同步

刘勇 谢勇

分数阶FitzHugh-Nagumo模型神经元的动力学特性及其同步

刘勇, 谢勇
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  • 通过对分数阶FitzHugh-Nagumo模型神经元的研究,当外加电流强度作为分岔参数时,发现这种模型神经元从静息态到周期放电态所经历的Hopf分岔点不同于相应的整数阶模型神经元的分岔点;而且分数阶FitzHugh-Nagumo模型神经元呈现周期放电的外加电流强度的范围比相应的整数阶模型神经元的范围小,然而放电频率却比相应的整数阶模型神经元的放电频率高.同时还揭示在周期放电的情况下分数阶FitzHugh-Nagumo模型神经元之间的同步速率比相应的整数阶模型神经元之间的同步速率快.在数值模拟分数阶微分方程
    • 基金项目: 国家自然科学基金(批准号:10502039,10602041)资助的课题.
    [1]

    [1] Zhu C X,ZOU Y 2009 Control and Decision 24 161 (in Chinese)[朱呈祥、邹云 2009 控制与决策 24 161]

    [2]

    [2] Bagley R L Calico R A 1999 Journal of Guidance,Control,and Dynamics 14 304

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    [3] Koeller R C 1984 Acta Mechanica 58 299

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    [4] Koeller R C 1984 Journal of Applied Mechanics 51 299

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    [5] Skaar S B,Michel A N,Miller R K 1988 IEEE Transactionson on Automatic Control 3(4) 348

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    [6] Ichise M,Nagayanay Y,Kojima T 1971 Journal of Electroa-nalytical Chemistry Interfacial Electrochemisry 33 253[7] Sun H H,Onaral B,Tsao Y Y 1984 IEEE Transactions on Ciomedical Engineering 31 664

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    [8] Sun H H,Abdelwahed A A,Onaral B 1984 IEEE Tranactions on Automatic Control 29 441

    [8]

    [9] Mark R J,Hall M W 1981 IEEE Trans.Acoust,Speech Signal Processing 29 872[10]Podlubny I 1999 Fractional Differential Equations(San Diego.CA:Academic Press)

    [9]

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

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    ]Wheatcraft S W,Benson D A,Meerschaert M M 2000 Water Resour.Res. 36 1413

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    ]Mandelbrot B 1967 IEEE Transactions on Information Theory 13 289

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    ]Lin R 2007 Ph. D. Dissertation(Xiamen Univ.) (in Chinese)[林然 2007 博士学位论文(厦门大学)]

    [13]

    ]Deng W H 2007 Ph. D. Dissertation (Shanghai Univ.) (in Chinese)[邓伟华 2007 博士学位论文(上海大学)]

    [14]

    ]Che Y Q 2005 Thesis for the Masters Degree (Tianjin Univ.) (in Chinese)[车艳秋 2005 硕士学位论文(天津大学)]

    [15]

    ]Xie Y,Xu J X,Kang Y M,Hu S J,Duan Y B 2003 Acta Phys. Sin. 52 1112 (in Chinese)[谢勇、徐建学、康艳梅、胡三觉、段玉斌 2003 物理学报 52 1112]

    [16]

    ]Lu Q S,Liu S Q,Liu F,Wang Q Y,Hou Z H,Zheng Y H 2008 Advances in Mechanics 38 766 (in Chinese)[陆启韶、刘深泉、刘峰、王青云、侯中怀、郑艳红 2008 力学进展 38 766]

    [17]

    ]Yu H J,Tong W J 2009 Acta Phys. Sin. 58 2977 (in Chinese)[于洪洁、童伟君 2009 物理学报 58 2977]

    [18]

    ]Zhang H,Fang L P,Tong Q Y 2007 Acta Phys. Sin. 56 7339 (in Chinese)[张宏、方路平、童勤业 2007 物理学报 56 7339]

    [19]

    ]Naundorf B,Wolf F,Volgushev M 2006 Nature 440 1060

    [20]

    ]Auastasio T J 1994 Biol.Cybern. 72 69[23]Lundstrom B N,Higgs M H,Spain W J,Fairhall A L 2008 Nature Neuroscience 11 1335

    [21]

    ]Malek M H,Hashemi S R IFMBE Proceedings 21 825

    [22]

    ]Xie Y,Chen L,Kang Y M,Aihara K 2008 Phys. Rev. E 77 061921

    [23]

    ]Xie Y,Aihara K,Kang Y M 2008 Phys. Rev. E 77 021917

    [24]

    ]Wang Q Y,Shi X,Lu Q S 2008 Synchronization dynamics in the coupled system of neurons (Beijing:Science Press)p4 (in Chinese)[王青云、石霞、陆启韶 2008 神经元耦合系统的同步动力学(北京:科学出版社)第4页]

    [25]

    ]Wen T,Tan X K,Yin S J 2003 Acta Physiologica Sinica 55 663 (in Chinese)[文挺、覃星奎、尹世金、韩丹 2003 生理学报 55 663]

    [26]

    ]Wang Q Y,Lu S Q 2008 Journal of Dynamics and Control 6 35 (in Chinese)[王青云、陆启韶 2008 动力学与控制学报 6 35]

    [27]

    ]Li H Q,Xu W,Wang C Q,Liu X D 2008 Acta Biophysica Sinica 24 29 (in Chinese)[李海泉、徐伟、王朝庆、刘小丹 2008生物物理学报 24 29]

    [28]

    ]Wang H X,Lu Q S 2006 Journal of Beijing University of Aeronautics and Astronautics 32 320 (in Chinese)[王海霞、陆启韶 2006 北京航空航天大学学报 32 320]

    [29]

    ]Wu Y,Xu J X,Jin W Y 2005 Journal of Xian Jiaotong University 39 544 (in chinese)[吴莹、徐建学、靳伍银 2005 西安交通大学学报 39 544]

    [30]

    ]Wu Y,Xu J X,He D H,Jin W Y 2005 Acta Phys. Sin. 54 3457 (in Chinese)[吴莹 、徐建学、何岱海、靳伍银 2005 物理学报 54 3457]

    [31]

    ]Zhao P D,Zhang X D 2008 Acta Phys. Sin. 57 2791 (in Chinese)[赵品栋、张晓丹 2008 物理学报 57 2791]

    [32]

    ]Matignon D 1996 IMACS, IEEE-SMC,Lille,France 963

    [33]

    ]Ahmed E,El2Sayed A M A,Elsaka H A A 2007 J. Math. Anal. Appl. 325 542

    [34]

    ]Zhang G J,Xu J X 2005 Acta Phys. Sin. 54 0557 (in Chinese)[张广军、徐建学 2005 物理学报 54 0557]

    [35]

    ]Zhang Y J 2009 Journal of Dynamics and Control 7 19 (in Chinese)[张艳娇、李美生、陆启韶 2009 动力学与控制报 7 19]

  • [1]

    [1] Zhu C X,ZOU Y 2009 Control and Decision 24 161 (in Chinese)[朱呈祥、邹云 2009 控制与决策 24 161]

    [2]

    [2] Bagley R L Calico R A 1999 Journal of Guidance,Control,and Dynamics 14 304

    [3]

    [3] Koeller R C 1984 Acta Mechanica 58 299

    [4]

    [4] Koeller R C 1984 Journal of Applied Mechanics 51 299

    [5]

    [5] Skaar S B,Michel A N,Miller R K 1988 IEEE Transactionson on Automatic Control 3(4) 348

    [6]

    [6] Ichise M,Nagayanay Y,Kojima T 1971 Journal of Electroa-nalytical Chemistry Interfacial Electrochemisry 33 253[7] Sun H H,Onaral B,Tsao Y Y 1984 IEEE Transactions on Ciomedical Engineering 31 664

    [7]

    [8] Sun H H,Abdelwahed A A,Onaral B 1984 IEEE Tranactions on Automatic Control 29 441

    [8]

    [9] Mark R J,Hall M W 1981 IEEE Trans.Acoust,Speech Signal Processing 29 872[10]Podlubny I 1999 Fractional Differential Equations(San Diego.CA:Academic Press)

    [9]

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

    [10]

    ]Wheatcraft S W,Benson D A,Meerschaert M M 2000 Water Resour.Res. 36 1413

    [11]

    ]Mandelbrot B 1967 IEEE Transactions on Information Theory 13 289

    [12]

    ]Lin R 2007 Ph. D. Dissertation(Xiamen Univ.) (in Chinese)[林然 2007 博士学位论文(厦门大学)]

    [13]

    ]Deng W H 2007 Ph. D. Dissertation (Shanghai Univ.) (in Chinese)[邓伟华 2007 博士学位论文(上海大学)]

    [14]

    ]Che Y Q 2005 Thesis for the Masters Degree (Tianjin Univ.) (in Chinese)[车艳秋 2005 硕士学位论文(天津大学)]

    [15]

    ]Xie Y,Xu J X,Kang Y M,Hu S J,Duan Y B 2003 Acta Phys. Sin. 52 1112 (in Chinese)[谢勇、徐建学、康艳梅、胡三觉、段玉斌 2003 物理学报 52 1112]

    [16]

    ]Lu Q S,Liu S Q,Liu F,Wang Q Y,Hou Z H,Zheng Y H 2008 Advances in Mechanics 38 766 (in Chinese)[陆启韶、刘深泉、刘峰、王青云、侯中怀、郑艳红 2008 力学进展 38 766]

    [17]

    ]Yu H J,Tong W J 2009 Acta Phys. Sin. 58 2977 (in Chinese)[于洪洁、童伟君 2009 物理学报 58 2977]

    [18]

    ]Zhang H,Fang L P,Tong Q Y 2007 Acta Phys. Sin. 56 7339 (in Chinese)[张宏、方路平、童勤业 2007 物理学报 56 7339]

    [19]

    ]Naundorf B,Wolf F,Volgushev M 2006 Nature 440 1060

    [20]

    ]Auastasio T J 1994 Biol.Cybern. 72 69[23]Lundstrom B N,Higgs M H,Spain W J,Fairhall A L 2008 Nature Neuroscience 11 1335

    [21]

    ]Malek M H,Hashemi S R IFMBE Proceedings 21 825

    [22]

    ]Xie Y,Chen L,Kang Y M,Aihara K 2008 Phys. Rev. E 77 061921

    [23]

    ]Xie Y,Aihara K,Kang Y M 2008 Phys. Rev. E 77 021917

    [24]

    ]Wang Q Y,Shi X,Lu Q S 2008 Synchronization dynamics in the coupled system of neurons (Beijing:Science Press)p4 (in Chinese)[王青云、石霞、陆启韶 2008 神经元耦合系统的同步动力学(北京:科学出版社)第4页]

    [25]

    ]Wen T,Tan X K,Yin S J 2003 Acta Physiologica Sinica 55 663 (in Chinese)[文挺、覃星奎、尹世金、韩丹 2003 生理学报 55 663]

    [26]

    ]Wang Q Y,Lu S Q 2008 Journal of Dynamics and Control 6 35 (in Chinese)[王青云、陆启韶 2008 动力学与控制学报 6 35]

    [27]

    ]Li H Q,Xu W,Wang C Q,Liu X D 2008 Acta Biophysica Sinica 24 29 (in Chinese)[李海泉、徐伟、王朝庆、刘小丹 2008生物物理学报 24 29]

    [28]

    ]Wang H X,Lu Q S 2006 Journal of Beijing University of Aeronautics and Astronautics 32 320 (in Chinese)[王海霞、陆启韶 2006 北京航空航天大学学报 32 320]

    [29]

    ]Wu Y,Xu J X,Jin W Y 2005 Journal of Xian Jiaotong University 39 544 (in chinese)[吴莹、徐建学、靳伍银 2005 西安交通大学学报 39 544]

    [30]

    ]Wu Y,Xu J X,He D H,Jin W Y 2005 Acta Phys. Sin. 54 3457 (in Chinese)[吴莹 、徐建学、何岱海、靳伍银 2005 物理学报 54 3457]

    [31]

    ]Zhao P D,Zhang X D 2008 Acta Phys. Sin. 57 2791 (in Chinese)[赵品栋、张晓丹 2008 物理学报 57 2791]

    [32]

    ]Matignon D 1996 IMACS, IEEE-SMC,Lille,France 963

    [33]

    ]Ahmed E,El2Sayed A M A,Elsaka H A A 2007 J. Math. Anal. Appl. 325 542

    [34]

    ]Zhang G J,Xu J X 2005 Acta Phys. Sin. 54 0557 (in Chinese)[张广军、徐建学 2005 物理学报 54 0557]

    [35]

    ]Zhang Y J 2009 Journal of Dynamics and Control 7 19 (in Chinese)[张艳娇、李美生、陆启韶 2009 动力学与控制报 7 19]

  • 引用本文:
    Citation:
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出版历程
  • 收稿日期:  2009-05-10
  • 修回日期:  2009-06-02
  • 刊出日期:  2010-03-15

分数阶FitzHugh-Nagumo模型神经元的动力学特性及其同步

  • 1. 西安交通大学航天航空学院强度与振动教育部重点实验室,西安 710049
    基金项目: 

    国家自然科学基金(批准号:10502039,10602041)资助的课题.

摘要: 通过对分数阶FitzHugh-Nagumo模型神经元的研究,当外加电流强度作为分岔参数时,发现这种模型神经元从静息态到周期放电态所经历的Hopf分岔点不同于相应的整数阶模型神经元的分岔点;而且分数阶FitzHugh-Nagumo模型神经元呈现周期放电的外加电流强度的范围比相应的整数阶模型神经元的范围小,然而放电频率却比相应的整数阶模型神经元的放电频率高.同时还揭示在周期放电的情况下分数阶FitzHugh-Nagumo模型神经元之间的同步速率比相应的整数阶模型神经元之间的同步速率快.在数值模拟分数阶微分方程

English Abstract

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