Asymptotic and exact solutions of the Fitzhugh-Nagumo model

DOI10.1134/S1560354718020028zbMath1401.34004OpenAlexW2802730536WikidataQ129967207 ScholiaQ129967207MaRDI QIDQ1799399

Nikolay A. Kudryashov

Publication date: 18 October 2018

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1560354718020028

zbMATH Keywords

exact solutionFitzHugh-Nagumo modelneuronsystem of equationsPainelevé test

Mathematics Subject Classification ID

Neural biology (92C20) Nonlinear ordinary differential equations and systems (34A34) Explicit solutions, first integrals of ordinary differential equations (34A05) Singular perturbations for ordinary differential equations (34E15)

Related Items (12)

A nearly exact discretization scheme for the FitzHugh-Nagumo model ⋮ A priori estimates for solutions of FitzHugh-Rinzel system ⋮ Unnamed Item ⋮ Exact solutions and integrability of the Duffing-van der Pol equation ⋮ Unnamed Item ⋮ Exact solutions of the equation for surface waves in a convecting fluid ⋮ On solutions to a FitzHugh-Rinzel type model ⋮ A remark on the meromorphic solutions in the FitzHugh-Nagumo model ⋮ Painlevé analysis and a solution to the traveling wave reduction of the Radhakrishnan-Kundu-Lakshmanan equation ⋮ Analytical Properties and Solutions of the FitzHugh – Rinzel Model ⋮ On Integrability of the FitzHugh – Rinzel Model ⋮ An analytical scheme on complete integrability of 2D biophysical excitable systems

Cites Work

• One method for finding exact solutions of nonlinear differential equations
• Popular ansatz methods and solitary wave solutions of the Kuramoto-Sivashinsky equation
• Application of simplest equations of Bernoulli and Riccati kind for obtaining exact traveling-wave solutions for a class of PDEs with polynomial nonlinearity
• Paul Painlevé and his contribution to science
• Solitary wave solution for the generalized Kawahara equation
• A note on solutions of the generalized Fisher equation
• Analytical properties of nonlinear dislocation equation
• Simplest equation method to look for exact solutions of nonlinear differential equations

This page was built for publication: Asymptotic and exact solutions of the Fitzhugh-Nagumo model