一类时延反馈神经网络的稳定性及吸引域的估计

STABILITY OF A CLASS OF FEEDBACK NEURAL NETWORKS WITH TIME-DELAY AND THE ESTIMATION OF DOMAIN OF ATTRACTION

反馈型神经网络由于具有极为丰富的动力学行为和整体计算能力（如优化、联想、振荡和混饨）而倍受关注，近几年的研究表明，当网络的时延足够小时，具有延时的对称Hopfield型神经网络和无时延情况一样也是全局稳定的．本文通过构造适当Lyapunov泛函的方法，对一类具有时延的反馈型神经网络平衡点的渐近稳定性进行了分析，得到了平衡点渐近稳定的充分条件：要检验一个有时间延迟的反馈型神经网络的稳定性，只要测试一个特定矩阵的定性性质或一个特定不等式即可．最后我们也提供了一种估计网络渐近稳定平衡点吸引域的方法．

In recent years, the feedback neural networks have attracted consider-able attention because of their rich dynamical behavior and collected computationalability, such as optimization, associative memory, oscillation and chaos, etc.. Ithas been indicated that the symmetric Hopfield neural networks with time-delay areglobally asymptotic stability if the time-delay is enough small, as well as the neuralnetworks without time-delay. This paper discusses asymptotic stability of equilibri-um point for a class of feedback neural networks with time - delay via the methodof constructing suitable Lyapunov functional, and obtain the sufficient conditionsfor asymptotic stability of equilibrium point. These criteria to test asymptotic sta-bility of the equilibrium of these time-delay feedback neural networks require verifi-cation of the definiteness of a certain matrix or verification of a certain inequality.This paper proposes also a method of estimating the domain of attraction of equilib-rium point of the time-delay neural networks.