Localized nonlinear waves in a myelinated nerve fiber with self-excitable membrane

doi:10.1088/1674-1056/ac720d

中国物理B ›› 2023, Vol. 32 ›› Issue (2): 20504-020504.doi: 10.1088/1674-1056/ac720d

Localized nonlinear waves in a myelinated nerve fiber with self-excitable membrane

Nkeh Oma Nfor^1,2,†, 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

收稿日期:2022-04-09 修回日期:2022-05-08 接受日期:2022-05-23 出版日期:2023-01-10 发布日期:2023-01-10
通讯作者: Nkeh Oma Nfor E-mail:omnkeh@gmail.com

Localized nonlinear waves in a myelinated nerve fiber with self-excitable membrane

Nkeh Oma Nfor^1,2,†, 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

Received:2022-04-09 Revised:2022-05-08 Accepted:2022-05-23 Online:2023-01-10 Published:2023-01-10
Contact: Nkeh Oma Nfor E-mail:omnkeh@gmail.com

摘要/Abstract

摘要： 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.

关键词: myelinated nerve, Fitzhugh-Nagumo, capacitive feedback parameter, Ginzburg-Landau, collision, annihilation

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.

Key words: myelinated nerve, Fitzhugh-Nagumo, capacitive feedback parameter, Ginzburg-Landau, collision, annihilation

中图分类号: (Solitons)

05.45.Yv

Nkeh Oma Nfor, Patrick Guemkam Ghomsi, and Francois Marie Moukam Kakmeni. Localized nonlinear waves in a myelinated nerve fiber with self-excitable membrane[J]. 中国物理B, 2023, 32(2): 20504-020504.

Nkeh Oma Nfor, Patrick Guemkam Ghomsi, and Francois Marie Moukam Kakmeni. Localized nonlinear waves in a myelinated nerve fiber with self-excitable membrane[J]. Chin. Phys. B, 2023, 32(2): 20504-020504.

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Localized nonlinear waves in a myelinated nerve fiber with self-excitable membrane

Localized nonlinear waves in a myelinated nerve fiber with self-excitable membrane

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