Abstract: The existence and uniqueness of the equilibrium point and its global asymptotic are discussed for a class of neural networks with time-varying delays.The neural networks model includes the delayed Hopfield neural network，delayed Cellular neural network，and Cohen-Grossberg neural network as its special cases.Several new sufficient conditions for ascertaining the existence，uniqueness of the equilibrium point，global asymptotic stability of such neural networks are obtained by using the Brouwer’s fixed point theory and constructing suitable Lyapunov functions.The new criteria don’t require the activation functions to be differentiable，bounded，monotone nondecreasing.Two illustrative examples are given to demonstrate the effectiveness of the obtained results.

Key words: time-varying delays, neural networks, equilibrium point, global asymptotic stability

摘要： 讨论了一类广义时变时滞递归神经网络的平衡点的存在性、唯一性和全局指数稳定性。这个神经网络模型包括时滞Hopfield神经网络，时滞Cellular神经网络，时滞Cohen-Grossberg神经网络作为特例。基于微分不等式技术，利用Brouwer不动点定理并构造合适的Lyapunov函数，得到了保证递归神经网络的平衡点存在、唯一、全局指数稳定的新的充分条件。新的充分条件不要求激励函数的可微性、有界性和单调性，同时减少了对限制条件的要求。两个仿真例子表明了所得结果的有效性。

关键词: 时变时滞, 神经网络, 平衡点, 全局渐近稳定