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    A weak condition for global stability of delayed neural networks

    Access Status
    Open access via publisher
    Authors
    Luo, R.
    Xu, Honglei
    Wang, W.
    Sun, Jie
    Xu, W.
    Date
    2016
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Luo, R. and Xu, H. and Wang, W. and Sun, J. and Xu, W. 2016. A weak condition for global stability of delayed neural networks. Journal of Industrial and Management Optimization. 12 (2): pp. 505-514.
    Source Title
    Journal of Industrial and Management Optimization
    DOI
    10.3934/jimo.2016.12.505
    ISSN
    1547-5816
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/40445
    Collection
    • Curtin Research Publications
    Abstract

    The classical analysis of asymptotical and exponential stability of neural networks needs assumptions on the existence of a positive Lyapunov function V and on the strict negativity of the function dV=dt, which often come as a result of boundedness or uniformly almost periodicity of the activation functions. In this paper, we investigate the asymptotical stability problem of Hopfield neural networks with time delays under weaker conditions. By constructing a suitable Lyapunov function, sufficient conditions are derived to guarantee global asymptotical stability and exponential stability of the equilibrium of the system. These conditions do not require the strict negativity of dV=dt, nor do they require that the activation functions to be bounded or uniformly almost periodic.

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