By using the various scale expansions in the
semi-discrete approximation, we analytically derived the complex
Ginzburg-Landau equation from the Li'enard version of the discrete FitzHugh
Nagumo model. The FHN model, characterised by a recovery mechanism, provides us
with a better understanding of the basic dynamics of membrane potential
interaction and captures the general properties of an excitable membrane in a
qualitative manner. The complex equation of GinzburgLandau now governs the
dynamics of pulse propagation along a myelinated nerve fibre in which the
relationship of wave dispersion is used to describe the famous propagation
failure and saltatory conduction phenomena. The pulse soliton solution stability analysis
that mimics the action potential follows the Benjamin-Feir criterion for plane
wave solutions. Finally , the results of our computational simulations indicate
that the nerve impulse extends as the dissipation rises along the myelinated
axon and gradually degenerates to front solutions.
Author(s) Details
N. Oma Nfor
Department of Physics, HTTC Bambili, University of Bamenda, P. O. Box 39
Bambili-Cameroon.
M. T. Mokoli
View Book :- https://bp.bookpi.org/index.php/bpi/catalog/book/301
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