Bifurcation and Stability of Stationary Solutions of the Fitz-Hugh-Nagumo Equations

The Fitz-Hugh-Nagumo equations have been of some interest to both mathematicians and theoretical biologists for several years. The reason for this stems from the fact that they can be considered as a simpler model for the celebrated Hodgkin-Huxley equations, in that they exhibit many of the features of this latter system. Indeed, mathematicians have studied them because their structure is different from the usually encountered equations in physics, and they therefore admit solutions with less familiar properties: homoclinic travelling waves, threshold effects, etc. The equations can be written as