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Localized nonlinear waves in a myelinated nerve fiber with self-excitable membrane |
| Nkeh Oma Nfor1,2,†, Patrick Guemkam Ghomsi2, and Francois Marie Moukam Kakmeni2 |
1 Department of Physics, HTTC Bambili, University of Bamenda, P. O. Box 39 Bambili, Cameroon;
2 Complex Systems and Theoretical Biology Group, 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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Abstract We systematically study the evolution of modulated nerve impulses in a myelinated nerve fiber, where both the ionic current and membrane capacitance provide the necessary nonlinear feedbacks. This is achieved by using a perturbation technique, in which the Liénard form of the modified discrete Fitzhugh-Nagumo equation is reduced to the complex Ginzburg-Landau amplitude equation. Three distinct values of the capacitive feedback parameter are considered. At the critical value of the capacitive feedback parameter, it is shown that the dynamics of the system is governed by the dissipative nonlinear Schrödinger equation. Linear stability analysis of the system depicts the instability of plane waves, which is manifested as burst of modulated nerve impulses that fulfills the Benjamin-Feir criteria. Variations of the capacitive feedback parameter generally influences the plane wave stability and hence the type of wave profile identified in the neural network. Results of numerical simulations mainly confirm the propagation, collision, and annihilation of nerve impulses in the myelinated axon.
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Received: 09 April 2022
Revised: 08 May 2022
Accepted manuscript online: 23 May 2022
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PACS:
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05.45.Yv
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(Solitons)
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Corresponding Authors:
Nkeh Oma Nfor
E-mail: omnkeh@gmail.com
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Cite this article:
Nkeh Oma Nfor, Patrick Guemkam Ghomsi, and Francois Marie Moukam Kakmeni Localized nonlinear waves in a myelinated nerve fiber with self-excitable membrane 2023 Chin. Phys. B 32 020504
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