Channelopathies affecting potassium chanels are a recognized cause of neuronal hyperexcitability, observed in certain pathologies. From a computational perspective, their study can be approached with the reduced Rinzel model, derived from the classical Hodgkin-Huxley model. In this work we analyze how the decrease in potassium chanels conductance modifies neuron membrane potencial using Rinzel non-linear equations. Numerical simulations are performed in Python using fourth order Runge-Kutta method. Besides, through an analysis from the dynamic systems perspective, changes between control case and pathological one can be interpreted as a shift in the phase plane of fixed points, nullclines and limit cycles. We found that in the pathological situation, bifurcations appears with lower values of external current. Thus, the studied model qualitatively reproduces neuronal hiperexcitability, and allows a mathematical interpretation. This enables linking ion chanelopatties with excitability phenomena.