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时滞惯性神经网络的稳定性和分岔控制

朱霖河 赵洪涌

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时滞惯性神经网络的稳定性和分岔控制

朱霖河, 赵洪涌

Stability and bifurcation control in inertial neuron networks with delays

Zhu Lin-He, Zhao Hong-Yong
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  • 针对一类二阶时滞惯性神经网络模型,提出一种基于时滞反馈的分岔控制方法. 利用时滞微分方程动力学理论,给出反馈控制系统的稳定性以及发生Hopf分岔的判别条件. 数值仿真显示所设计的控制器不仅能有效延迟网络分岔的发生,还能扩大稳定域并改善网络的收敛速度.
    Based on the second order delay inertia neural network model, this paper puts forward the bifurcation control method: delay feedback control method. Applying the theory of delay differential equations, we give some stability and Hopf bifurcation conditions for the feedback control system. Examples are given to validate that the feedback controller can control the occurrence of bifurcation effectively, expand the stability domain, and change the convergence speed of the network as well.
    • 基金项目: 国家自然科学基金重点项目(批准号:11032009)、国家自然科学基金(批准号:61174155)和江苏省青蓝工程基金资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61174155), the Key Program of the National Natural Science Foundation of China (Grant No. 11032009), and the Qing Lan Project of Jiangsu, China.
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    Wheeler D W, Schieve W C 1997 Physica D 105 267

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    Yi L, Zhou X, Wu Y, Zhou M 2006 Chaos, Solitons & Fractals 29 190

    [13]

    Zhao H, Chen L, Yu X 2011 Acta Phys. Sin. 60 070202 (in Chinese) [赵洪涌, 陈凌, 于小红 2011 物理学报 60 070202]

    [14]

    Yang X, Yang F 2004 Chaos, Solitons & Fractals 20 587

    [15]

    Li C, Chen G, Liao X 2004 The European Physical Journal B 41 337

    [16]

    Liao X, Li S, Wong K 2003 Nonlinear Dynamics 31 299

    [17]

    Liu Q, Liao X, Guo S, Wu Y 2009 Nonlinear Analysis 10 2384

    [18]

    Liu Z, Li C, Liu J 1997 Acta Acustica 22 297 (in Chinese) [刘镇清, 李成林, 刘江伟 1997 声学学报 22 297]

    [19]

    Jiang M, Lin B, Yuan B 1998 Signal Processing 14 331 (in Chinese) [江铭虎, 林碧琴, 袁保宗1998 信号处理 14 331]

    [20]

    Zeng Q, Song A, Huang W 1999 J of Southeast University 29 25 (in Chinese) [曾庆军, 宋爱国, 黄惟一 1999 东南大学学报 29 25]

    [21]

    Ellman R, Cooke K 1963 Differential-Difference Equations (New York Academic Press)

  • [1]

    Hopfield J 1984 Proc. Nat. Acad. Sci. 41 3088

    [2]

    Yang Z, Xu D 2005 IEEE Trans. Circu. Syste. 52 517

    [3]

    Liao X, Chen G, Sanchez E N 2002 Neural Networks 15 855

    [4]

    Wang L, Xu D 2003 Science in China 46 466

    [5]

    Cao J, Xiao M 2007 IEEE Trans. Neural Net. 18 416

    [6]

    Kwon O, Kwon J, Kim S 2011 Chin. Phys. B 20 050505

    [7]

    Lee S, Kwon O, Park J 2010 Chin. Phys. B 19 050507

    [8]

    Li H, Liao X, Huang H 2011 Acta Phys. Sin. 60 020512 (in Chinese) [李华青, 廖晓峰, 黄宏宇 2011 物理学报 60 020512]

    [9]

    Wang H, Yu J 2001 Acta Phys. Sin. 50 2303 (in Chinese) [王宏霞, 虞厥邦 2001 物理学报 50 2303]

    [10]

    Wang Z, Zhang H, Wang L 2006 Acta Phys. Sin. 55 2687 (in Chinese) [王占山, 张化光, 王智良 2006 物理学报 55 2687]

    [11]

    Wheeler D W, Schieve W C 1997 Physica D 105 267

    [12]

    Yi L, Zhou X, Wu Y, Zhou M 2006 Chaos, Solitons & Fractals 29 190

    [13]

    Zhao H, Chen L, Yu X 2011 Acta Phys. Sin. 60 070202 (in Chinese) [赵洪涌, 陈凌, 于小红 2011 物理学报 60 070202]

    [14]

    Yang X, Yang F 2004 Chaos, Solitons & Fractals 20 587

    [15]

    Li C, Chen G, Liao X 2004 The European Physical Journal B 41 337

    [16]

    Liao X, Li S, Wong K 2003 Nonlinear Dynamics 31 299

    [17]

    Liu Q, Liao X, Guo S, Wu Y 2009 Nonlinear Analysis 10 2384

    [18]

    Liu Z, Li C, Liu J 1997 Acta Acustica 22 297 (in Chinese) [刘镇清, 李成林, 刘江伟 1997 声学学报 22 297]

    [19]

    Jiang M, Lin B, Yuan B 1998 Signal Processing 14 331 (in Chinese) [江铭虎, 林碧琴, 袁保宗1998 信号处理 14 331]

    [20]

    Zeng Q, Song A, Huang W 1999 J of Southeast University 29 25 (in Chinese) [曾庆军, 宋爱国, 黄惟一 1999 东南大学学报 29 25]

    [21]

    Ellman R, Cooke K 1963 Differential-Difference Equations (New York Academic Press)

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  • PDF下载量:  790
  • 被引次数: 0
出版历程
  • 收稿日期:  2013-12-05
  • 修回日期:  2014-01-17
  • 刊出日期:  2014-05-05

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