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
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.
Received: 09 April 2022
Revised: 08 May 2022
Accepted manuscript online: 23 May 2022
PACS:
05.45.Yv
(Solitons)
Corresponding Authors:
Nkeh Oma Nfor
E-mail: omnkeh@gmail.com
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
[1] Nfor N O, Ghomsi P G and Moukam Kakmeni F M 2018 Phys. Rev. E97 022214 [2] Achu F G, Mkam S E, Moukam Kakmeni F M and Tchawoua C 2018 Phys. Rev. E98 022216 [3] Achu F G, Moukam Kakmeni F M and Dikandé A M 2018 Phys. Rev. E97 012211 [4] Nfor N O and Mokoli M T 2016 J. Mod. Phys.7 1166 [5] Moukam Kakmeni F M, Inack E M and Yamakou E M 2014 Phys. Rev. E89 052919 [6] Dikandé A M and Bartholomew G A 2009 Phys. Rev. E80 041904 [7] Keener J 1980 SIAM J. Appl. Math.39 528 [8] Murray J D 2002 Mathematical Biology II: Spatial Models and Biomedical Applications, 3rd edn (Berlin: Springer-Verlag) [9] Hodgkin A L and Huxley A F 1945 J. Physiol.104 176 [10] Hodgkin A L and Huxley A F 1952 J. Physiol.117 500 [11] FitzHugh R A 1961 Biophys. J.1 445 [12] Nagumo J, Arimoto S and Yoshitzawa S 1962 Proc. IRE50 2061 [13] Sherwood L 2001 Human Physiology: From Cells to Systems 4th edn (Brooks and Cole Publishers) [14] Takashima S 1979 Biophys. J.26 133 [15] Tasaki I and Matsumoto G 2002 Bull. Math. Biol.64 1069 [16] Tuckwell H C 1979 Science205 493 [17] Nfor N O, Serge B S and Moukam Kakmeni F M 2021 Chin. Phys. B30 020502 [18] Etémé A S, Tabi C B, Ateba J F B, Ekobena H P F, Mohamadou A and Kofane T C 2018 J. Phys. Commun.2 125004 [19] Tabi C B, Ondoua R Y, Fouda H P E and Kofané T C 2016 Phys. Lett. A380 2374 [20] Mvogo A, Ndzana F II and Kofané T C 2019 Wave Motion84 46 [21] Wang L, Wu X and Zhang H Y 2018 Phys. Lett. A382 2650 [22] Wang L, Liu C, Wu X, Wang X and Sun W R 2018 Nonlinear Dyn.94 977 [23] Lan Z Z and Su J J 2019 Nonlinear Dyn.96 2535 [24] Kong L Q, Wang L, Wang D S, Dai C Q, Wen X Y and Xu L 2019 Nonlinear Dyn.98 691 [25] Toda M 1967 J. Phys. Soc. Jpn.23 501 [26] Hirota R and Suzuki K 1970 J. Phys. Soc. Jpn.28 1366 [27] Hirota R and Suzuki K 1973 Proc. IEEE61 1483 [28] Pandey S N, Bindu P S, Senthilvelan M and Lakshmanan M 2009 J. Math. Phys.50 102701 [29] Banerjee D and Bhattacharjee J K 2010 J. Phys. A: Math. Theor.43 062001 [30] Messias M and Gouveia M R A 2011 Physica D240 1402 [31] Dauxois T and Peyrard M 2006 Physics of Solitons (New York: Cambridge University Press) [32] Kuramoto Y 1984 Chemical Oscillations, Waves, and Turbulence (Berlin: Springer) [33] Pismen L M 1999 Vortices in Nonlinear Fields (Oxford: Oxford University/Clarendon Press) [34] Tchawoua C 2005 Ph.D. Dessertation (Université de Yaoundé I) [35] Giannini J A and Joseph R I 1990 IEEE J. Quantum Electron.26 2109 [36] Marquié R, Bilbault J M and Remoissenet M 1995 Physica D87 371 [37] Kengne E, Lakhssassi A and Liu W M 2015 Phys. Rev. E91 062915 [38] Benjamin T B and Feir J E 1967 J. Fluid Mech.27 417 [39] Karlsson M 1995 J. Opt. Soc. Am. B12 2071 [40] Takahashi N, Hanyu Y, Musha T, Kubo R and Matsumoto G 1990 Physica D43 318 [41] Nozaki K and Bekki N 1984 J. Phys. Soc. Jpn.53 1581 [42] Pereira N R and Stenflo L 1977 Phys. Fluids20 1733 [43] Lautrup B, Appali R, Jackson A and Heimburg T 2011 Eur. Phys. J. E34 1 [44] Houssaini K E, Ivanov A I, Bernard C and Jirsa V K 2015 Phys. Rev. E91 010701 [45] Acker C D, Kopell N and White J A 2003 J. Comput. Neurosci.15 71 [46] Poznanski R R, Cacha L A, Al-Wesabi Y M S, Ali J, Bahadoran M, Yupapin P P and Yunus J 2017 Sci. Rep.7 2746 [47] Nguyen J N V, Dyke P, Luo D, Malomed B A and Hulet R G 2014 Nat. Phys.10 918 [48] Rotermund H H, Jakubith S, Oertzen A V and Ertl G 1991 Phys. Rev. Lett.66 3083 [49] Tasaki I 1999 Jpn. J. Physiol.49 125 [50] Ueda T, Muratsugu M, Inoue I and Kobatake Y 1974 J. Membr. Biol.18 177 [51] Mvogo A, Tambue A, Germain H, Ben-Bolie and Kofané T C 2016 Commun. Nonlinear Sci. Numer. Simulat.39 396
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
