Frequency Response Characterization of Coupled Hodgkin-Huxley Neurons in Kuramoto-Inspired Oscillator Network

Abstract

Synchronization in networks of conductance-based neurons depends on the external stimulus, coupling architecture, coupling strength, and initial state of the constituent cells. In this work, we numerically investigate a finite all-to-all network of identical Hodgkin–Huxley (HH) neurons coupled through a normalized diffusive membrane-voltage term. The purpose is not to introduce a new neuronal model but to provide a joint finite-time characterization of the membrane voltage and the three ionic gating variables during the development of collective activity. Synchronization is quantified from pairwise state differences using matrix norms, whereas the short-time Fourier transform (STFT) and continuous wavelet transform (CWT) representations are used to describe the time-localized spectral content of the simulated trajectories. For the investigated parameter values and initial conditions, the coupled network exhibits convergence toward a common resting state, a transient single-spike response, sustained oscillatory responses, and transient intervals of reduced coherence followed by more coordinated firing. Increasing the applied current changes the observed response regime and dominant spectral component. Within the finite simulation windows considered here, the frequency estimates obtained from both time–frequency methods also show a small decreasing trend with an increase in coupling strength. This trend is reported as a numerical observation rather than as a universal asymptotic property because its magnitude may depend on the observation window, initial conditions, network size, and frequency-estimation procedure. The results illustrate how voltage coupling affects both the convergence of neuronal trajectories and the finite-time spectral characteristics of the membrane and gating-variable responses.