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The analog circuit design of the memristive neural network (MNN), which can automatically perform the online learning algorithm, is an open question. In this article, a memristive self-learning neuron circuit for implementing the online least mean square (LMS) algorithm is designed. Extending on the designed neuron circuit, the circuit implementation of the monolayer and multilayer neural network is proposed. The proposed neural network can automatically converge the output to the set target according to the input. The application-level validations of the circuits are done using pattern recognition and license plate detection. The performances of the designed MNN circuits and the effect of memristive variation are analyzed through PSPICE simulations. The learning accuracy of the proposed circuit for license plate detection can reach 93%. Circuit simulation results reveal that the proposed MNN circuits can accelerate the training speed and have the tolerance to the variations of the memristor. [ABSTRACT FROM AUTHOR]