Abstract
By employing the invariant manifold theory developed by Fenichel, singularly perturbed dynamical systems are analysed with a special emphasis on then as multiple time scale systems. Exposition of the theory is guided by an example, the celebrated Hodgkin-Huxley Equatrons. More specifically, a geometric approach is given to the construction of homoclinic orbits which represent travelling pulses on nerve axons. In this approach, Exchange Lemma, together with Fenichel-normal forms, plays the decisive role.
