Author(s)

Nkeh Oma Nfor¹, Mebu Tatason Mokoli²

¹Complex Systems and Theoretical Biology Group, Laboratory of Research on Advanced Materials and Nonlinear Science(LaRAMaNS), Department of Physics, Faculty of Science,University of Buea, Buea, Cameroon.
²Laboratory of Research on Advanced Materials and Nonlinear Science (LaRAMaNS), Department of Physics, Faculty of Science, University of Buea, Buea, Cameroon.

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.

Ginzburg-Landau Equation, Liénard Form, Fitz Hugh Nagumo Model, Semidiscrete Approximation, Saltatory Conduction, Benjamin-Feir Criteria, Dissipation

Oma Nfor, N. and Mokoli, M. (2016) Dynamics of Nerve Pulse Propagation in a Weakly Dissipative Myelinated Axon. Journal of Modern Physics, 7, 1166-1180. doi: 10.4236/jmp.2016.710106.