Neurons, being electrically excitable cells, are highly susceptible to external electric fields. Motivated by previous studies on silent Hodgkin–Huxley neurons under zero external current, we numerically investigate how an extremely low-frequency external electric field influences the dynamics of a silent Hodgkin–Huxley neuron under varying levels of external (injected) DC current. Our results show that, in addition to previously reported subthreshold oscillations, \(p\!:\!q\) mode-locking (where p spikes occur per q cycles of stimulation), and chaotic behaviors at zero external current, increasing the external current gives rise to additional dynamical regimes, including quasi-periodic oscillations and shifts in the location of the maximum firing rate as the current approaches the critical value \(I_{\textrm{ext}} \approx 9.7~\mathrm {\mu A/cm^2}\) . The emergence of these behaviors depends on the external electric field parameters and the level of external current. Analysis of the largest Lyapunov exponent revealed that chaotic states arise near the threshold amplitude in the absence of external current, whereas such states are rarely observed at larger amplitudes \(V_0 > 7~\textrm{mV}\) . These findings extend earlier studies by highlighting the crucial role of external current in shaping the nonlinear dynamical responses of silent Hodgkin–Huxley neurons to extremely low-frequency electric fields.
