BIFURCATION-ANALYSIS OF THE TRAVELING WAVE-FORM OF FITZHUGH-NAGUMO NERVE-CONDUCTION MODEL EQUATION

The FitzHugh-Nagumo model for travelling wave type neuron excitation i s studied in detail. Carrying out a linear stability analysis near the equilibrium point, we bring out various interesting bifurcations whic h the system admits when a specific L-2 symmetry is present and when i t is not. Based on a center manifold reduction and normal form analysi s, the Hopf normal form is deduced. The condition for the onset of lim it cycle oscillations is found to agree well with the numerical result s. We further demonstrate numerically that the system admits a period doubling route to chaos both in the presence as well as in the absence of constant external stimuli. (C) 1997 American Institute of Physics.