Dynamics of a Neuromorphic Circuit Incorporating a Second-Order Locally Active Memristor and Its Parameter Estimation

Neuromorphic circuits emulate the brain’s massively parallel, energy-efficient, and robust information processing by reproducing the behavior of neurons and synapses in dense networks. Memristive technologies have emerged as key enablers of such systems, offering compact and low-power implementations. In particular, locally active memristors (LAMs), with their ability to amplify small perturbations within a locally active domain to generate action potential-like responses, provide powerful building blocks for neuromorphic circuits and offer new perspectives on the mechanisms underlying neuronal firing dynamics. This paper introduces a novel second-order locally active memristor (LAM) governed by two coupled state variables, enabling richer nonlinear dynamics compared to conventional first-order devices. Even when the capacitances controlling the states are equal, the device retains two independent memory states, which broaden the design space for hysteresis tuning and allow flexible modulation of the current–voltage response. The second-order LAM is then integrated into a FitzHugh–Nagumo neuron circuit. The proposed circuit exhibits oscillatory firing behavior under specific parameter regimes and is further investigated under both DC and AC external stimulation. A comprehensive analysis of its equilibrium points is provided, followed by bifurcation diagrams and Lyapunov exponent spectra for key system parameters, revealing distinct regions of periodic, chaotic, and quasi-periodic dynamics. Representative time-domain patterns corresponding to these regimes are also presented, highlighting the circuit’s ability to reproduce a rich variety of neuronal firing behaviors. Finally, two unknown system parameters are estimated using the Aquila Optimization algorithm, with a cost function based on the system’s return map. Simulation results confirm the algorithm’s efficiency in parameter estimation.