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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.

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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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