Modular memristor model with synaptic-like plasticity and volatile memory

Abstract Compact models of memristors are essential for simulating large-scale neuromorphic systems, yet they often do not include description of complex dynamics like volatile relaxation and synaptic plasticity. We introduce a modular, computationally efficient memristor model that bridges this gap by integrating principles from physics and computational neuroscience. Starting from standard memristive system dynamics, the framework incorporates synaptic-like plasticity dynamics, a mapping from state variables to cumulative conductance, a volatility module, and a saturation module. The plasticity component is inspired by a biological rule for spike-timing-dependent plasticity (STDP) and is compatible with the general memristive systems formalism. Finally, we propose a Laplace transform-based technique to derive the precise form of the mapping from state variables to cumulative conductance, replacing ad hoc voltage-current relationships with principled construction. We quantitatively evaluate the model against experimental data from the presently studied carbazole-based polymer memristor, which exhibits potentiation, synaptic-like plasticity, and volatile decay. The resulting compact model keeps the core, plasticity, cumulative-conductance, volatility, and saturation modules explicit and provides a practical framework for device-specific simulation and further validation.