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具反应扩散项的脉冲时滞Cohen-Grossberg神经网络的稳定性
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国家自然科学基金(60904028;61174077)


Stability analysis for impulsive reaction-diffusion Cohen-Grossberg neural networks with time-varying delays
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    摘要:

    讨论了一类具反应扩散项的脉冲变时滞Cohen-Grossberg神经网络在Neu-mann边界条件下的稳定性.通过构造分片连续的Lyapunov函数,结合Neumann特征值问题,并利用Gronwall-Bellman脉冲积分不等式,得到了新的与反应扩散项和时滞有关的保证平衡点全局指数稳定性的代数判据.

    Abstract:

    This work concerns the stability for a class of impulsive Cohen-Grossberg neural networks with time-varying delays,reaction-diffusion and Neumann boundary condition.By means of the impulsive integral inequality of Gronwall-Bellman type and piecewise continuous Lyapunov functions as well as Neumann eigenvalue problem,we summarize some new and concise sufficient conditions ensuring the global exponential stability of the equilibrium point.Moreover,the provided stability criteria are shown to be associated with both reaction-diffusion and time delays.An illustrative example is finally given to demonstrate the effectiveness of our obtained results.

    参考文献
    [1] Cohen M A,Grossberg S.Absolute stability of global pat-tern formation and parallel memory storage by competitiveneural networks[J].IEEE Trans Syst Man Cybern,1983,13:815-826
    [2] Cao J,Liang L.Boundedness and stability for Cohen-Grossberg neural network with time-varying delays[J].JMath Anal Appl,2004,296(2):665-685
    [3] Cao J,Wang J.Globally exponentially stability and perio-dicity of recurrent neural networks with time delays[J].IEEE Trans Circuits Syst,2005,52(5):920-931
    [4] Liu X Z.Stability results for impulsive differential systems with applications to population growth models[J].Dynamical Systems,1994,9(2):163-174
    [5] Liu X Z,Wang Q.Impulsive stabilization of high-orderhopfield-type neural networks with time-varying delays
    [J].IEEE Transactions on Neural Networks,2008,19(1):71-79
    [6] Yang Z,Xu D.Impulsive effects on stability of Cohen-Grossberg neural networks with variable delays[J].Ap-plied Mathematics and Computation,2006,177(1):63-78
    [7] Arik S,Orman Z.Global stability analysis of Cohen-Grossberg neural networks with time varying delays[J].Physics Letter A,2005,341(5/6):410-421
    [8] Huang T,Li C,Chen G.Stability of Cohen-Grossbergneural networks with unbounded distributed delays[J].Chaos,Solitons＆Fractals,2007,34(3):992-996
    [9] Liao X,Li C,Wong K.Criteria for exponential stability of Cohen-Grossberg neural networks[J].Neural Network,2004,17(10):1401-1414
    [10] Zhang J,Suda Y,Komine H.Global exponential stabilityof Cohen-Grossberg neural networks with variable delays
    [J].Physics Letter A,2005,338(1):44-50
    [11] Chen Z,Ruan J.Global stability analysis of impulsive Co-hen-Grossberg neural networks with delay[J].PhysicsLetter A,2005,345(1/2/3):101-111
    [12] Chen Z,Ruan J.Global dynamic analysis of general Co-hen-Grossberg neural networks with impulse[J].Chaos,Solitons and Fractals,2007,32:1830-1837
    [13] Yang Z,Xu D.Impulsive effects on stability of Cohen-Grossberg neural networks with variable delays[J].Ap-plied Mathematics and Computation,2006,177(1):63-78
    [14] Song Q,Zhang J.Global exponential stability of impulsiveCohen-Grossberg neural network with time-varying delays
    [J].Nonlinear Analysis-Real World Applications,2008,9(2):500-510
    [15] Chen Z,Ruan J.Global dynamic analysis of general Co-hen-Grossberg neural networks with impulse[J].Chaos,Solitons＆Fractals,2007,32:1830-1837
    [16] Wan L,Zhou Q.Convergence analysis of stochastic hy-brid bidirectional associative memory neural networkswith delays[J].Phys Lett A,2007,370(5/6):423-432
    [17] Zhou Q,Wan L,Sun J.Exponential stability of reaction-diffusion generalized Cohen-Grossberg neural networkswith time-varying delays[J].Chaos,Solitons＆Fractals,2007,32:1713-1719
    [18] Li K,Song Q.Exponential stability of impulsive Cohen-Grossberg neural networks with time-varying delays andreaction-diffusion terms[J].Neurocomputing,2008,72(1/2/3):231-240
    [19] Liu P,Yi F,Yang J,et al.Analysis on global exponentialrobust stability of reaction-diffusion neural networks with Stype distributed delays[J].Physica D-Nonlinear Phe-nomina,2008,237(4):475-485
    [20] Lou X,Cui B.Boundedness and exponential stability fornonautonomous cellular neural networks with reaction-dif-fusion terms[J].Chaos,Solitons＆Fractals,2007,33(2):653-662
    [21] Lu J.Global exponential stability and periodicity of reac-tion-diffusion delayed recurrent neural networks withDirichlet boundary conditions[J].Chaos,Solitons＆Fractals,2008,35(1):116-125
    [22] Lv Y,Lv W,Sun J.Convergence dynamics of stochasticreaction-diffusion recurrent neural networks with continu-ously distributed delays[J].Nonlinear Analysis-RealWorld Applications,2008,9(4):1590-1606
    [23] Qiu J.Exponential stability of impulsive neural networkswith time-varying delays and reaction-diffusion terms
    [J].Neurocomputing,2007,70(4/5/6):1102-1108
    [24] Wang L,Gao Y.Global exponential robust stability of re-action-diffusion interval neural networks with time-varying delays[J].Physics Letter A,2006,350(5/6):342-348
    [25] Zhao H,Wang K.Dynamical behaviors of Cohen-Gross-berg neural networks with delays and reaction-diffusionterms[J].Neurocomputing,2006,70:536-543
    [26] Pan J,Liu X Z,Zhong S M.Stability criteria for impulsivereaction-diffusion Cohen-Grossberg neural networks withtime-varying delays[J].Mathematical and ComputerModelling,2010,51(9/10):1037-1050
    [27] Lakshmikantham V,Bainov D D,Simeonov P S.Theory of218张雨田,等.具反应扩散项的脉冲时滞Cohen-Grossberg神经网络的稳定性.ZHANG Yutian,et al.Stability analysis for impulsive reaction-diffusion Cohen-Grossberg neural networks with time-varying delays.impulsive differential equations[M].Singapore:World Scientific,1989
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张雨田,章旻慧.具反应扩散项的脉冲时滞Cohen-Grossberg神经网络的稳定性[J].南京信息工程大学学报(自然科学版),2012,4(3):213-219
ZHANG Yutian, ZHANG Minhui. Stability analysis for impulsive reaction-diffusion Cohen-Grossberg neural networks with time-varying delays[J]. Journal of Nanjing University of Information Science & Technology, 2012,4(3):213-219

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