中文摘要：

忆阻是近年来新发现的一类非线性电子元件．与通常的电阻不同，忆阻的阻值会随着通过的电流量的大小和方向不同而改变．这个特性使得忆阻具有了记忆的功能，在很多方面有着广泛的应用．该文给出了简化的忆阻的数学模型，基于该模型构造了时滞神经网络，利用微分包含理论、Lyapunov方法和同胚映射原理研究了其全局渐近稳定性问题，确保模型平衡点存在性、唯一性和一致全局渐近稳定性的充分条件被获得．最后提供的具有仿真的例子验证了获得的理论结果．

英文摘要：

Memristor is a newly prototyped nonlinear circuit device. Its value is not unique and changes according to the value of the magnitude and polarity of the voltage applied to it. Due to this feature, the memristor has the function of memory and broad potential applications of memristors have been reported in various fields. A simplified mathematical model was proposed to characterize the pinched hysteresis feature of the memristor and a memristor-based recurrent neural network model was given. With the theory of differential inclusion, Lyapunov approach and homeomorphism theory, the existence and uniqueness of the equilibrium point of the model were obtained, and the global uniform asymptotic stability of memristor-based recurrent neural networks was also obtained. Finally, the simulation result shows the efficiency of the theorem.