Action potentials are a crucial physiological event for body regulation and sensory information detection. This study represented a modification of FitzHugh-Nagumo model as a neutral delay differential equation. We proposed three nonlinear models and a linear model that explain the interaction between the time delays of the effects on the membrane potential and the stimulated current. To detect Hopf bifurcation, we determined fixed points and calculated eigenvalues. We identified regions of stability, instability, and oscillatory solutions for the proposed models. This paper shows how changing certain parameters can change the way a system works, how stable nerve firing is, and what role the time delay of the response to the stimulating current plays in nerve impulse firing. Gaining this understanding is critical for building diagnostic models and potential treatments for neurological disorders characterized by irregular firing patterns. We performed numerical simulations of the proposed models. Regular spike neurons have a strong tendency to adapt to large time delays of the stimulating current, whereas intrinsic bursting neurons make rapid spikes. Chattering neurons respond to the stimulating current with high-frequency bursts but exhibit moderate time delays in their responses. Fast-growing neurons, in contrast, show a rapid firing rate at high frequencies. Low-threshold neurons adapt significantly to high frequencies with only a low time delay to stimulation, which gives lots of insight into the dynamics of neuronal firing. Significantly, the time delay affects the stability or oscillatory solutions of the proposed models, and it is necessary for the critical role of synchronization between distinct brain loops and circuits.