Abstract
Using bifurcation analysis methods for dynamical systems, we investigated the influence of key physiological parameters \(-\) the intracellular and extracellular concentrations of sodium and potassium ions \(-\) on the stability of the fundamental mathematical model of neuronal excitability. Numerical calculations performed in MATLAB and MATCONT revealed Hopf bifurcations, indicating qualitative changes in neuronal behavior at critical equilibrium potentials of the respective ions. The conclusions drawn from this study may be useful for theoretical research related to neuronal potentials, as well as for developing therapeutic methods for various neurological disorders caused by alterations in extracellular (or intracellular) potassium or sodium concentrations, such as ischemic stroke, migraines, and traumatic injuries.
