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.
N. Oma Nfor
Department of Physics, HTTC Bambili, University of Bamenda, P. O. Box 39 Bambili-Cameroon.
M. T. Mokoli
Laboratory of Research on Advanced Materials and Nonlinear Science (LaRAMaNS), Department of Physics, Faculty of Science, University of Buea, P. O. Box 63 Buea, Cameroon.
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