Many memristors fabricated by different materials share the characteristics which are similar to the memory and learning functions of synapse in biological systems. These characteristics include memorizing and forgetting function and learning-experience behavior. A memristor model was proposed in the published paper [Chen L, Li C D, Huang T W, Chen Y R, Wen S P, Qi J T 2013 Phys. Lett. A 377 3260] to describe the memorizing and forgetting function of this kind of memristor. This model includes three state variables , and . The change of w describes the variation of the conductance of the memristor, a function fE () is used to the input voltage's influence on the change of , and are used to describe the its forgetting effect. The simulation analyses of this model in the published papers [Chen L, Li C D, Huang T W, Hu X F, Chen Y R 2016 Neurocomputing 171 1637] and [Meng F Y, Duan S K, Wang L D, Hu X F, Dong Z K 2015 Acta Phys. Sin. 64 148501] showed that this model can also describe the learning-experience behavior. This model is further studied in this paper to show its detailed characteristics. The analyses of the state equations of the original model show that these state equations cannot restrict the state variables in their permissible interval because the window function is not appropriately used in all the state equations, and the original window function cannot force the state equation to be identical to zero either when corresponding state variable reaches its bound. An improved window function is introduced and the appropriate utilization of this window function is discussed to deal with this problem. The upper bound of is defined in the modified model to describe the saturation of that has been observed in the experimental studies of this kind of memristor. The behaviors of the modified state equations are different from those of the original ones only when the state variables reach their bounds, and this modified model has the same ability to describe the memristor's memorizing and forgetting function and learning-experience behavior as original one. The behaviors of the model when the input voltage is not negative are discussed based on the state equations and their analytical solution when the input is the repeated voltage pulses, and the results of the discussion are used to explain how a model designed according to the memorizing and forgetting function can also describe the learning-experience behavior. The analysis shows that the increased rising speed of the state variable w in the stimulating process is caused by increasing the values of and , and the learning-experience behavior described by this model would also be influenced by the value of :a smaller initial value of state variable in the learning-experience experiment would lead to a more obvious learning-experience behavior. The analytical results are also used to design an estimation method based on the learning-experience experiment to estimate the parameters and function in the state equation. The further discussion shows that this proposed estimation method can also be used to verify the reasonability of the assumption used in the state equations that the derivatives of and are proportional to fE (V).