A model of a myelinated nerve axon: threshold behaviour and propagation

DOI10.1007/BF00276561zbMath0579.92004WikidataQ52679074 ScholiaQ52679074MaRDI QIDQ1068012

Sleeman, Brian D., Peter Grindrod

Publication date: 1985

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

zbMATH Keywords

global stabilitybehaviourthresholdwave frontstransmembrane potentialFitzHugh-Nagumo dynamicsmyelinated nerve axonsnodes of Ranvierperiodic steady state solutionpropagation of a superthreshold solution

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Physiological, cellular and medical topics (92Cxx)

Related Items (7)

Asymptotic behavior and steady state solutions of a myelinated axon model with Fitzhugh-Nagumo dynamics ⋮ Propagation of excited state and its failure in a simple model of myelinated nerve axons ⋮ Complex dynamics in one-dimensional nonlinear Schrödinger equations with stepwise potential ⋮ A mathematical study of effects of narrow gap width in myelinated nerve axons ⋮ Multiplicity of periodic solutions for differential equations arising in the study of a nerve fiber model ⋮ Complex dynamics in a nerve fiber model with periodic coefficients ⋮ Some aspects of the Morris-Lecar model and the myelinated axon models with Morris-Lecar dynamics

Cites Work

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• Threshold conditions for a diffusive model of a myelinated axon
• Geometric theory of semilinear parabolic equations
• Time-periodic solutions to semilinear parabolic equations

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