分布时滞Hopfield神经网络稳定性

针对分布时滞的Hopfield型神经网络构造了李雅普诺夫能量函数,证明了该网络的稳定性问题。证明过程中运用了引理的结论,充分利用了所取李雅普诺夫函数的特殊性,较多地运用了不等式分析方法及不等式放缩技巧。同时由于时滞的存在,证明过程中还涉及李雅普诺夫泛函问题。最后利用引理的结论得出了该网络全局一致渐近稳定的结论。

Stability of Hopfield Type Neural Network with Distributed Time Delay

In this paper, Lyapunov energy function is constructed according to the Hopfield type neural network with infinite time delay. The stability of the network is proved using the Lyap-unov energy function. In the course of proving, the conclusion of lemma and the particularity of the function that is gotten is fully utilized. Some inequality analysis methods and inequality enlarg-ing and narrowing techniques are used. The Lyapunov functional is also invoved because of the existence of time delay.In the end, the conclusion of global consistent asymptotic stability for the network is drawn from the lemma.