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

doi:10.1088/1674-1056/ae4c6b

Abstract This paper presents a second-order memcapacitor ($C_{\rm M}$)-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 two-parameter 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 second-order 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.

Keywords: second-order memcapacitor FitzHugh-Nagumo neuron firing dynamics neuromorphic computing

Received: 19 December 2025
Revised: 26 February 2026
Accepted manuscript online: 03 March 2026

PACS:	05.45.Tp	(Time series analysis)
	87.19.ld	(Electrodynamics in the nervous system)
	05.90.+m	(Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems)
	05.45.-a	(Nonlinear dynamics and chaos)

Fund: This project is supported by the National Natural Science Foundation of China (Grant No. 62171401) and the Key Project of the Education Department of Hunan Province (Grant No. 25A0146).

Corresponding Authors: Zhijun Li, Pengyang Li
E-mail: lizhijun@xtu.edu.cn;1936260040@qq.com

Cite this article:

Zhijun Li(李志军), and Pengyang Li(李鹏洋), Firing dynamics in a second-order memcapacitor-based FitzHugh-Nagumo neuron with multiscale memory 2026 Chin. Phys. B 35 060505

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

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