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Properties that are similar to the memory and leaing functions in biological systems have been observed and reported in the experimental studies of memristors fabricated by different materials.These properties include the forgetting effect,the transition from short-term memory (STM) to long-term memory (LTM),leaing-experience behavior,etc.The mathematical model of this kind of memristor would be very important for its theoretical analysis and application design.In our analysis of the existing memristor model with these properties,we find that some behaviors of the model are inconsistent with the reported experimental observations.A phenomenological memristor model is proposed for this kind of memristor.The model design is based on the forgetting effect and STM-to-LTM transition since these behaviors are two typical properties of these memristors.Further analyses of this model show that this model can also be used directly or modified to describe other experimentally observed behaviors.Simulations show that the proposed model can give a better description of the reported memory and leaing behaviors of this kind of memristor than the existing model.