TITLE:
Dynamics of Nerve Pulse Propagation in a Weakly Dissipative Myelinated Axon
AUTHORS:
Nkeh Oma Nfor, Mebu Tatason Mokoli
KEYWORDS:
Ginzburg-Landau Equation, Liénard Form, Fitz Hugh Nagumo Model, Semidiscrete Approximation, Saltatory Conduction, Benjamin-Feir Criteria, Dissipation
JOURNAL NAME:
Journal of Modern Physics,
Vol.7 No.10,
June
21,
2016
ABSTRACT: We analytically derived the complex Ginzburg-Landau equation from the Liénard form of the discrete FitzHugh Nagumo model by employing the multiple scale expansions in the semidiscrete approximation. 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 show that as the dissipation along the myelinated axon increases, the nerve impulse broadens and finally degenerates to front solutions.