Accurate computation of the stable solitary wave for the FitzHugh-Nagumo equations

DOI10.1007/BF00276063zbMath0479.92005OpenAlexW2163036037WikidataQ113909186 ScholiaQ113909186MaRDI QIDQ1161696

Robert M. Miura

Publication date: 1982

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00276063

zbMATH Keywords

Hodgkin-Huxley equationstravelling wave equationswave integrals

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Initial-boundary value problems for second-order parabolic equations (35K20) Error bounds for boundary value problems involving PDEs (65N15) Applications to the sciences (65Z05) Physiological, cellular and medical topics (92Cxx)

Related Items (16)

Stability of traveling waves: dichotomies and eigenvalue conditions on finite intervals ⋮ Resolvent Estimates for Boundary Value Problems on Large Intervals Via the Theory of Discrete Approximations ⋮ Implicit-explicit methods for reaction-diffusion problems in pattern formation ⋮ Computation and Stability of Traveling Waves in Second Order Evolution Equations ⋮ Numerical computation of heteroclinic orbits ⋮ Numerical evidence for global bifurcations leading to switching phenomena in long Josephson junctions ⋮ One way traffic of pulses in a neuron ⋮ Finding eigenvalues of holomorphic Fredholm operator pencils using boundary value problems and contour integrals ⋮ Computational electrocardiology: mathematical and numerical modeling ⋮ Nerve pulse transmission: Recovery variable and rate-type effects ⋮ The slow wave solution to the FitzHugh-Nagumo equations ⋮ Projective and coarse projective integration for problems with continuous symmetries ⋮ Mathematical modelling of weakly nonlinear pulses in a retinal neuron ⋮ Dynamics of Patterns in Nonlinear Equivariant PDEs ⋮ The stability of traveling calcium pulses in a pancreatic acinar cell ⋮ Wavefront propagation in an activation model of the anisotropic cardiac tissue: Asymptotic analysis and numerical simulations

Uses Software

• COLSYS
• CADRE

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local stability theory of the nerve impulse
• Automatic Computation of Nerve Excitation—Detailed Corrections and Additions
• Collocation Software for Boundary-Value ODEs
• Boundary Value Problems on Semi-Infinite Intervals and Their Numerical Solution
• ON THE EXISTENCE OF HOMOCLINIC AND PERIODIC ORBITS FOR THE FITZHUGH-NAGUMO EQUATIONS
• The Korteweg–deVries Equation: A Survey of Results
• Perturbation analysis of an approximation to the Hodgkin-Huxley theory
• A numerical and theoretical study of certain nonlinear wave phenomena
• A Collocation Solver for Mixed Order Systems of Boundary Value Problems
• Single and Multiple Pulse Waves for the FitzHugh–Nagumo

This page was built for publication: Accurate computation of the stable solitary wave for the FitzHugh-Nagumo equations