Firing dynamics in a second-order memcapacitor-based FitzHugh–Nagumo neuron with multiscale memory

Abstract This paper presents a second-order memcapacitor ( C M )-based FitzHugh–Nagumo (FHN) neuron model designed to emulate multiscale memory mechanisms observed in biological neurons. The memcapacitor incorporates two internal state variables — a fast variable that enables rapid response and a slow variable that enables gradual adaptation — replacing the linear membrane capacitor in the classical FHN circuit to form a four-dimensional neuronal system. The electrical activities of the neuron are systematically investigated using bifurcation diagrams, Lyapunov exponents, and a twoparameter dynamical map. Numerical simulations reveal that variations in excitation frequency and amplitude can induce transitions among chaotic firing, multiperiodic firing, and single-periodic spiking. Furthermore, the model demonstrates pronounced multistability governed by the memcapacitor’s initial states, where distinct periodic and chaotic attractors coexist within separate basins of attraction — a direct manifestation of the multiscale memory interaction. By tailoring external stimuli and internal parameters, the neuron successfully reproduces eight quintessential neuromorphic behaviors, including phasic and tonic spiking, mixed-mode oscillations, subthreshold oscillations, inhibition-induced spiking, rebound spikes, bistability, and Class 2 excitability. Finally, an analog FHN circuit integrated with a secondorder memcapacitor emulator is implemented using off-the-shelf electronic components. Circuit simulations demonstrate excellent agreement with numerical analyses, thereby validating both the model’s correctness and its physical realizability for neuromorphic engineering applications.