Dynamical mechanism of neuronal firing in the Hodgkin-Huxley model

The Hodgkin-Huxley (H-H) model remains a cornerstone in the study of neuronal dynamics, yet a global understanding of its behavior, particularly regarding transitions between silent, bistable, and repetitive firing states, has been limited. In this study, we employ the cell mapping method to systematically investigate the global dynamics of the H-H model under varying external currents —— an approach that overcomes the limitations of traditional local analysis methods. Our analysis reveals two critical novel findings, a previously unrecognized bistable regime at high currents and the “reversion to silence” phenomenon where the neuron returns to a silent state under extremely high currents. The results indicate that the model’s states are governed by the emergence and disappearance of distinct attractors as external current varies, with state transitions exhibiting asymmetric dynamics. Additionally, the system exhibits extreme sensitivity to initial conditions, particularly in bistable regimes. These findings advance our understanding of neuronal excitability, with implications for neuroengineering and clinical neuromodulation, and offer a robust framework for exploring global dynamics in nonlinear neuronal systems.