Research Article

Investigation of Hyperbolic Type Solutions of the Fitzhugh-Nagumo Model in Neuroscience

Volume: 1 Number: 1 June 30, 2023
EN TR

Investigation of Hyperbolic Type Solutions of the Fitzhugh-Nagumo Model in Neuroscience

Abstract

This article aims to obtain analytical solutions of the Fitzhugh – Nagumo (FN) model, which has an important place in neuroscience. The 1/G' - expansion method is used to obtain the solutions. Hyperbolic type travelling wave solutions are produced by using the 1/G'- expansion method, which is an effective and efficient method in solving nonlinear partial differential equations (NLPDEs). Then 3D, 2D and contour graphs are presented using a computer program.

Keywords

Fitzhugh – Nagumo model , hyperbolic type solution , 1/G'-expansion method.

References

  1. A. H. Bhrawy, ‘‘A Jacobi–Gauss–Lobatto collocation method for solving generalized Fitzhugh–Nagumo equation with time-dependent coefficients’’, Applied Mathematics and Computation, vol. 222, pp. 255-264, Oct. 2013, doi.org/10.1016/j.amc.2013.07.056.
  2. A. Yokus, ‘‘On the exact and numerical solutions to the FitzHugh–Nagumo equation’’, International Journal of Modern Physics B, vol. 34, no 17,2050149, Jun. 2020, doi.org/10.1142/S0217979220501490.
  3. H. Li and Y. Guo, ‘‘New exact solutions to the Fitzhugh–Nagumo equation’’, Applied Mathematics and Computation, vol. 180, no 2, pp. 524-528, Sep. 2006, doi.org/10.1016/j.amc.2005.12.035.
  4. M. Dehghana, J. M. Heris and A. Saadatmandi, ‘‘Application of semi‐analytic methods for the Fitzhugh–Nagumo equation, which models the transmission of nerve impulses’’, Mathematical Methods in the Applied Sciences, vol. 33, no 11, pp. 1384-1398, Jun. 2010, doi.org/10.1002/mma.1329.
  5. S. Duran, ‘‘An investigation of the physical dynamics of a traveling wave solution called a bright soliton’’, Physica Scripta, vol. 96, no 12, 125251, Nov. 2021, doi.org/10.1088/1402-4896/ac37a1.
  6. A. Yokus and M. A. Isah, ‘‘Stability analysis and solutions of (2+1)-Kadomtsev–Petviashvili equation by homoclinic technique based on Hirota bilinear form’’, Nonlinear Dynamics, vol. 109, no 4, pp. 3029-3040, Jun. 2022, doi.org/10.1007/s11071-022-07568-3.
  7. A. Yokus and M. A. Isah, ‘‘Investigation of internal dynamics of soliton with the help of traveling wave soliton solution of Hamilton amplitude equation’’, Optical and Quantum Electronics, vol. 54, no 8, pp. 528, Jul. 2022, doi.org/10.1007/s11082-022-03944-w.
  8. S. Duran, H. Durur and A. Yokuş, ‘‘Traveling wave and general form solutions for the coupled Higgs system’’, Mathematical Methods in the Applied Sciences, vol. 46, no 8, pp. 8915-8933, Jan. 2023, doi.org/10.1002/mma.9024.
  9. S. S. Nourazar, M. Soori and A. Nazari-Golshan, ‘‘On the homotopy perturbation method for the exact solution of Fitzhugh–Nagumo equation’’, International Journal of Mathematics & Computation, vol. 27, no 1, pp. 32-43, 2016.
  10. H. Li and Y. Guo, ‘‘New exact solutions to the Fitzhugh–Nagumo equation’’, Applied Mathematics and Computation, vol. 180, no 2, pp. 524-528, Sep. 2006, doi.org/10.1016/j.amc.2005.12.035.
IEEE
[1]H. Durur, A. Aydın, and R. Arslantürk, “Investigation of Hyperbolic Type Solutions of the Fitzhugh-Nagumo Model in Neuroscience”, JSAT, vol. 1, no. 1, pp. 11–16, June 2023, doi: 10.5281/zenodo.8074822.