Memristor is a nonlinear two-terminal passive electronic component,which is proposed in recent years and is different from the resistor,capacitor and inductor.The memristor-based recurrent neural networks,with different system parameters,show all kinds of dynamic performances.We investigated global exponential periodicity problem in regard to a class of memristor-based recurrent neural networks with time-varying delays,and considered the symmetry and asymmetry situations of connection weights in switching state.Via the studying approach of constructing two proper Lyapunov functions,the Halanay inequality and the theory of differential equations with discontinuous right-hand sides introduced by Fillippov,we presented the sufficiency condition concerning the global exponential periodicity.Finally, experimental results verified the feasibility and effectiveness of the proposed theory.%忆阻器是近几年来提出的一种区别于电阻、电容、电感的一类非线性两端无源电子元件，而忆阻器递归神经网络由于系统参数的不同，系统表现出各种动态性能。针对一类变时滞忆阻器递归神经网络，研究全局指数周期性问题，考虑连接权值在切换状态下的对称和非对称的情况，通过构造两个 Lyapunov 函数、Halanay 不等式和由 Fillippov 给出的右端不连续微分方程理论的研究方法，提出关于全局指数周期性的充分性条件。最后，实验结果验证了所提理论的可行性和有效性。
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