A generalized FitzHugh-Nagumo equation

DOI10.1016/j.na.2006.12.001zbMath1135.35009OpenAlexW1994789319MaRDI QIDQ2470093

Yanyan Li

Publication date: 13 February 2008

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2006.12.001

zbMATH Keywords

numerical integrationmethod of linesLie group methodnerve-impulse propagation

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Neural biology (92C20) Invariance and symmetry properties for PDEs on manifolds (58J70) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Geometric theory, characteristics, transformations in context of PDEs (35A30) Solutions to PDEs in closed form (35C05) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items (7)

Autonomic learning via saturation gain method, and synchronization between neurons ⋮ Analytical and Simulation Results for the Stochastic Spatial Fitzhugh-Nagumo Model Neuron ⋮ Existence, uniqueness and a priori estimates for a nonlinear integro-differential equation ⋮ A simple spatial integration scheme for solving Cauchy problems of non-linear evolution equations ⋮ Unnamed Item ⋮ Qualitative analysis of bounded traveling wave solutions to Nagumo nerve conduction equation and its approximate oscillatory solutions ⋮ Multiple lump, generalized breathers, Akhmediev breather, manifold periodic and rogue wave solutions for generalized FitzHugh-Nagumo equation: applications in nuclear reactor theory

Uses Software

• DIMSYM
• LIE

Cites Work

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• Multidimensional nonlinear diffusion arising in population genetics
• Symmetry analysis of differential equations with MATHEMATICA
• DIMSYM and LIE: Symmetry determination packages
• Persistence of travelling wave solutions of a fourth order diffusion system
• A spike train with a step change in the interspike intervals in the FitzHugh-Nagumo model
• CNN model for studying dynamics and travelling wave solutions of FitzHugh-Nagumo equation
• Approximate conditional symmetries and approximate solutions of the perturbed Fitzhugh–Nagumo equation
• Nonlinear Effects in the Dynamics of Car Following
• Symmetry-based algorithms to relate partial differential equations: I. Local symmetries
• LIE, a PC program for Lie analysis of differential equations

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