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Stability and bifurcation control in inertial neuron networks with delays

Zhu Lin-He Zhao Hong-Yong

Stability and bifurcation control in inertial neuron networks with delays

Zhu Lin-He, Zhao Hong-Yong
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  • 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.
    • 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.
    [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)

  • [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)

  • [1] Yang Yong-Xia, Li Yu-Ye, Gu Hua-Guang. Synchronization transition from bursting to spiking and bifurcation mechanism of the pre-Bötzinger complex. Acta Physica Sinica, 2020, 69(4): 040501. doi: 10.7498/aps.69.20191509
    [2] Control of spiral waves in excitable media under polarized electric fields. Acta Physica Sinica, 2020, (): . doi: 10.7498/aps.69.20191934
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  • Received Date:  05 December 2013
  • Accepted Date:  17 January 2014
  • Published Online:  05 May 2014

Stability and bifurcation control in inertial neuron networks with delays

  • 1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Fund Project:  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.

Abstract: 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.

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