Small amplitude periodic waves for the FitzHugh-Nagumo equations

DOI10.1007/BF00275396zbMath0503.92008OpenAlexW2011733823WikidataQ52731341 ScholiaQ52731341MaRDI QIDQ1835598

Sleeman, Brian D.

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1007/bf00275396

zbMATH Keywords

Laplace transformFitz-Hugh-Nagumo equationsnerve impulsesmall amplitude periodic waves

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Periodic solutions to PDEs (35B10) Initial value problems for second-order parabolic equations (35K15) Physiological, cellular and medical topics (92Cxx)

Related Items (3)

Comparison principles for strongly coupled reaction-diffusion equations ⋮ Nerve pulse transmission: Recovery variable and rate-type effects ⋮ Singular perturbation analysis of bistable differential equation arising in the nerve pulse propagation

Cites Work

• On FitzHugh's nerve axon equations
• FitzHugh's nerve axon equations
• Local stability theory of the nerve impulse
• Repetitive activity and Hopf bifurcation under point-stimulation for a simple FitzHugh-Nagumo nerve conduction model
• A spectral radius theorem for matrix seminorms
• Boundary value problems for the Fitzhugh-Nagumo equations
• Critical manifolds, travelling waves, and an example from population genetics
• Nagumo's equation
• Some Mathematical Problems from Neurobiology
• Bursting Phenomena in Excitable Membranes
• Numerical studies of the laminar boundary layer for Mach numbers up to 15
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