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This work proposes a two-dimensional electrophysiological model fordescribing neuronal responses to external electric stimuli under patch-clampedconditions. Our proposed model successfully captures the key features of theHodgkin-Huxley model, while offering improved informativeness and numericalefficiency.  By analysing bifurcation diagrams from various reduced models, we describethe contributions of different ionic channels to the stability or instabilityof the neurones' response. We also explore the influence of various cellparameters in the neurone's spiking frequency, including the membranecapacitance and the ionic channels' conductivities and Nerst potentials.  Additionally, we suggest a spatial model for the axon that effectivelysimulates unidirectional signal transmission along neurons unaffected bymembrane potential perturbations. After analysing the characteristics of thiscompartmental model, including the impact of intracellular resistance andmembrane capacitance on the signal's velocity, we observed considerablediscrepancies between our findings and those predicted by the cable equationmodel for signal propagation.  Moreover, our investigation reveals that when the transmission of neuronalsignals occurs in multiple peaks, there is a transient variation in theirwavelength and frequency, resulting in different peak velocities. Furthermore,our findings consistently demonstrate that the first peak - in some cases, theonly peak observed - maintains a relatively constant velocity along the axonregardless of the stimulus intensity and is always faster than the subsequentpeaks.

The role of ion channels in the transmission of signals along axons