Studies on the Dynamics of Nerve Pulse Propagation in a Weakly Dissipative Myelinated Axon

We analytically derived the complex Ginzburg-Landau equation from the Li ´enard form of the discrete
FitzHugh Nagumo model, by employing the multiple scale expansions in the semidiscrete
approximation. The FHN model which is characterized by a recovery mechanism, furnishes us
with a better understanding of the essential dynamics of the interaction of membrane potential and
qualitatively captures the general properties of an excitable membrane. The complex Ginzburg-
Landau equation now governs the dynamics of a pulse propagation along a myelinated nerve
fiber where the wave dispersion relation is used to explain the famous phenomena of propagation
failure and saltatory conduction. Stability analysis of the pulse soliton solution that mimics the action
potential fulfills the Benjamin-Feir criteria for plane wave solutions. Finally, results from our numerical
simulations shows that as the dissipation along the myelinated axon increases, the nerve impulse
broadens and finally degenerate to front solutions.