摘要
在去掉对激励函数有界、连续可导、平均时滞有界的条件下,仅要求激励函数满足Lipschitz条件和连接权矩阵之间的关系是一个M-矩阵的情形下,利用重合度理论、Dini导数等知识得出了具周期输入的有限连续分布的一类细胞神经网络周期解的存在性.利用Dini导数和不等式分析技术在同样条件下得出了周期解的指数稳定性.推广和改进了前人的结论.并举例说明了所得定理的有效性.
Without assuming the boundedness, continuous, derivation of the active functions and the boundedness of the mean time-delay, the existence of a class of neural networks＇ periodic solution involving distributed delays with periodic inputs is obtained by using the theory of coincidence degree and the knowledge of Dini derivative, when the active functions satisfy the Lipchitz condition and the relations of the interconnection matrix is an M-matrix. Meanwhile, under the same conditions, the global exponential stability of neural networks＇ periodic solution is obtained by employing Dini derivative and the analysis technique of inequality. Some existing conclusions are improved, extended and complemented. An example is also worked out to demonstrate the advantages of these results.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2009年第1期170-178,共9页
Acta Mathematica Scientia
基金
国家自然科学基金(60374023)
湖南省教育厅重点课题(04A012)
湖南省自然科学基金(05JJ40093)资助
关键词
神经网络
周期解
连续分布时滞
全局指数稳定性.
Neural network
Periodic solution
Continuously distributed time-delay
Global exponential stability.
