| 引用本文: | 楼旭阳,崔宝同.具反应扩散混合时滞Cohen-Grossberg神经网络的指数耗散性[J].控制理论与应用,2008,25(4):619~622.[点击复制] |
| LOU Xu-yang,CUI Bao-tong.Exponential dissipativity of Cohen-Grossberg neural networks with mixed delays and reaction-diffusion terms[J].Control Theory and Technology,2008,25(4):619~622.[点击复制] |
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| 具反应扩散混合时滞Cohen-Grossberg神经网络的指数耗散性 |
| Exponential dissipativity of Cohen-Grossberg neural networks with mixed delays and reaction-diffusion terms |
| 摘要点击 1688 全文点击 1375 投稿时间：2007-03-06 修订日期：2007-08-25 |
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| DOI编号 10.7641/j.issn.1000-8152.2008.4.005 |
| 2008,25(4):619-622 |
| 中文关键词 神经网络 反应扩散 混合时滞 耗散性 M–矩阵 |
| 英文关键词 neural networks reaction-diffusion terms mixed delays dissipativity M–matrix |
| 基金项目 教育部科学技术研究重点项目(107058); 江苏省自然科学基金资助项目(BK2007016); 江苏省2007年研究生科研创新计划. |
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| 中文摘要 |
| 利用扩散算子特性、M–矩阵性质和不等式分析技巧, 在不要求神经网络激励函数的有界性、单调性、可微性以及平均时滞有界性的弱保守条件下, 研究了一类具有反应扩散混合时滞的非自治Cohen-Grossberg神经网络的实不变集、全局指数稳定性和指数耗散性, 并给出了相关的充分性条件. 文中所使用的方法摒弃了常规构造适当的Lyapunov泛函的方法, 克服了Lyapunov泛函难构造的困难, 且得到的结果扩展和改进了其他文献结果. 最后给出了一个数值例子来说明所得结果的有效性. |
| 英文摘要 |
| Without assuming the boundedness, monotonicity and differentiability of the activation functions and the boundedness of average time delays, the invariant set, global exponential stability and exponential dissipativity of a class of Cohen-Grossberg neural networks with mixed delays and reaction-diffusion terms are studied by employing the properties of diffusion operator, M–matrix and inequality technique. Some correlative sufficient conditions are then derived. The method used in this paper ignores the common requirement of constructing proper Lyapunov functionals, thus eliminating the difficulty in building proper Lyapunov functionals. Moreover, the results extend and improve the prior results in publications. Finally, a numerical example is given to illustrate the effectiveness of the results. |