Publication date: 21st July 2025
As neuromorphic computing moves toward energy-efficient, event-driven architectures,
the use of oscillator-based neurons has gained renewed interest. These systems aim to
emulate the core dynamic features of biological spiking neurons while leveraging
physical models that allow compact and tunable implementations. In this context, we
investigate a neuromorphic system governed by a set of two coupled differential
equations, structurally analogous to the Morris–Lecar model [1,2]. This reduced
framework captures key excitability and oscillatory features characteristic of spiking
neurons, while remaining analytically tractable.
By drawing a formal analogy with an elementary electrical circuit composed of a resistor,
a capacitor, and an inductor, we derive an analytical expression for the system’s
impedance function [3]. This complex function describes the linear frequency response
of the system to small periodic perturbations, and provides a natural bridge between the
time-domain dynamics of the model and its frequency-domain characteristics. The
impedance reveals how the system processes inputs across a range of frequencies,
exhibiting features such as resonance and phase lag.
Through numerical simulations, we explore how the system responds as a control
parameter is varied. We observe a Hopf bifurcation that marks the transition from a stable
fixed point to a regime of self-sustained oscillations [4]. Importantly, we find that this
bifurcation is accompanied by a qualitative transformation in the impedance spectrum:
the emergence of resonance peaks, frequency selectivity, and distinct shifts in phase
response signal the onset of oscillatory behavior. These changes reflect a reorganization
of the system’s internal time scales and nonlinear feedback structure.
Our findings underscore the utility of impedance spectroscopy as a diagnostic and
classification tool for neuromorphic oscillators. The method provides insight into critical
transitions—such as the onset of spiking—and allows identification of dynamical regimes
using experimentally accessible quantities. This approach is rooted in well-established
techniques from electrochemistry and neuroscience, where impedance measurements
have long been used to probe the behavior of both chemical and biological oscillators
This work was funded by the European Research Council (ERC) via Horizon Europe
Advanced Grant, grant agreement nº 101097688 (“PeroSpiker”), MENEU project
(20250002) by Universitat Poltècnica de València, (CEX2021-001230-S grant by
MCIN/AEI/10.13039/501100011033) of the Spanish Ministry of Science and Innovation
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