Memristor for Neuromorphic Applications: Models and Circuit Implementations

Since the first experimental evidence for the existence of the memristor in nature, a large number of memristor mathematical models have been proposed in the literature. Among them the generalized Boundary Condition Memristor model sticks out for the adaptability of the dynamics at the boundaries and for the tunability of the nonvolatile behavior. The first part of the paper describes in some detail the PSpice implementation of the generalized Boundary Condition Memristor model. Such PSpice emulator constitutes a reliable tool for computer-aided design of memristor-based circuits. As a conclusion to the first part, the use of the emulator demonstrates the ability of the memristor to capture the Hebbian learning rule, which governs the rate of change of synaptic strength in biological neural networks. The second part of the paper is devoted to the presentation of a novel class of purely passive memristor circuits. Each element from the class is composed of the cascade between a static nonlinear two-port and a linear dynamic one-port and employs solely standard electrical components from Circuit Theory. The state equations of the proposed circuits fall into the class of memristor systems.