Stability, periodicity, and mode-locking behaviors in a Hodgkin-Huxley neuron
The simple input-output dynamics of the Hodgkin-Huxley (HH) neuronal model was analyzed using a generic sinusoidal input consisting of a constant current density I0 modulated by a sinusoidal function with amplitude ΔI, and frequency f. The equations governing the HH model is then modified, numerically solved, and analyzed to understand the system's dynamical response. Power spectral density and neural coding techniques such as firing rate and vector strength were employed to observe the dynamics of the system. Using these mechanisms, mode-locking behaviors were observed in a stimulus-parameter plane that stabilizes as the constant bias is increased. An increasing number of action potentials and sustained periodicity measure is observed on mode-locking subregions in the parameter space (ΔI, ω). This proves that using frequency and temporal codings would still show similar characteristics of a neuron.