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An analytical scheme on complete integrability of 2D biophysical excitable systems

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  • Mondal, Argha
  • Mistri, Kshitish Ch.
  • Aziz-Alaoui, M.A.
  • Upadhyay, Ranjit Kumar

Abstract

We report a method to find the complete integrability and analytical scheme of a well-known two dimensional (2D) excitable biophysical system that includes a coupled non-linear ordinary differential equations (ODEs). We demonstrate the integrability of the autonomous FitzHugh–Nagumo (FHN) dynamical system for the time evolution equations of motion and briefly describe the solution procedure using the extended Prelle–Singer (PS) scheme without perturbation and series solution method. To illustrate the mathematical formulation procedure, both the time independent and time dependent integrals have been derived by using the extended PS method. Finally, the numerical solution of the integrals has been found with the original dynamical model. It also allows us to establish the integrability of another type of an analytical technique for the deterministic system and this explores the quantitative applicability of the method. Interestingly, the method may have significant applications in other physical systems.

Suggested Citation

  • Mondal, Argha & Mistri, Kshitish Ch. & Aziz-Alaoui, M.A. & Upadhyay, Ranjit Kumar, 2021. "An analytical scheme on complete integrability of 2D biophysical excitable systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    • Handle: RePEc:eee:phsmap:v:573:y:2021:i:c:s0378437121001965
    DOI: 10.1016/j.physa.2021.125924
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    References listed on IDEAS

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    1. D. Valenti & G. Augello & B. Spagnolo, 2008. "Dynamics of a FitzHugh-Nagumo system subjected to autocorrelated noise," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(3), pages 443-451, October.
    2. Agarwal, P. & Deni̇z, S. & Jain, S. & Alderremy, A.A. & Aly, Shaban, 2020. "A new analysis of a partial differential equation arising in biology and population genetics via semi analytical techniques," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    3. Odibat, Zaid, 2020. "An optimized decomposition method for nonlinear ordinary and partial differential equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
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