A phenomenological memristor model for short-term/long-term memory

• We take the Fick diffusion and the Soret diffusion into account in the ion drift theory.
• We develop a new model based on the old HP model.
• The new model can describe the forgetting effect and the spike-rate-dependent property of memristor.
• The new model can solve the boundary effect of all window functions discussed in [13].
• A new Hopfield neural network with the forgetting ability is built by the new memristor model.

Memristor is considered to be a natural electrical synapse because of its distinct memory property and nanoscale. In recent years, more and more similar behaviors are observed between memristors and biological synapse, e.g., short-term memory (STM) and long-term memory (LTM). The traditional mathematical models are unable to capture the new emerging behaviors. In this article, an updated phenomenological model based on the model of the Hewlett–Packard (HP) Labs has been proposed to capture such new behaviors. The new dynamical memristor model with an improved ion diffusion term can emulate the synapse behavior with forgetting effect, and exhibit the transformation between the STM and the LTM. Further, this model can be used in building new type of neural networks with forgetting ability like biological systems, and it is verified by our experiment with Hopfield neural network.