© World Scientific Publishing Company Memristor is a natural synapse because of its nanoscale and memory property, which influences the performance of memristive artificial neural networks. A three-variable memristor model is simplified with 15 kinds of properties, including the learning experience, the forgetting curve, the spiking time-dependent plasticity (STDP), the spiking rate dependent plasticity (SRDP), and the integration property. Through the analysis of the model, one more unobserved property called pseudo-polarity reversibility property is predicted by assuming the long-term memory is independent of memductance.