From pulses to plasticity: Analytical tools for memristive synapse design

Neuromorphic device design demands a clear understanding of the dynamics governing conductance modulation under external stimuli. Many synaptic memristors can be described by a quasi-linear model, where a memory variable relaxes between two limiting states. Here, we derive analytical expressions for the response of such systems to trains of voltage pulses, providing closed formulations for paired-pulse facilitation (PPF), convergent potentiation, and frequency-dependent gain. This approach predicts how the memory variable evolves toward stationary values determined by device and stimulation parameters, offering a compact alternative to numerical simulations. We experimentally validate the model using a nanofluidic memristor based on a nanoporous membrane, showing that the predicted convergence closely matches measured potentiation and that the analytical PPF trends reproduce experimental data. These results establish a unified framework for describing spike-driven plasticity and enable reliable cross-comparison of synaptic behavior across memristive systems, facilitating their integration into neuromorphic circuits.