Existence and stability of periodic travelling wave solutions to Nagumo's nerve equation

DOI10.1007/BF00275838zbMath0456.92012OpenAlexW2069406986WikidataQ113909252 ScholiaQ113909252MaRDI QIDQ1150539

Kenjiro Maginu

Publication date: 1980

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

Full work available at URL: https://doi.org/10.1007/bf00275838

zbMATH Keywords

existencetravelling wavesNagumo equationnerve axon equationPoincare index

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Wave equation (35L05) Physiological, cellular and medical topics (92Cxx)

Related Items (10)

Instability of small-amplitude periodic waves from fold-Hopf bifurcation ⋮ Instability of periodic traveling wave solutions in a modified Fitzhugh-Nagumo model for excitable media ⋮ Branching of double pulse solutions from single pulse solutions in nerve axon equations ⋮ Stability properties of traveling pulse solutions of the higher dimensional FitzHugh-Nagumo equations ⋮ Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system ⋮ Near-pulse solutions of the FitzHugh-Nagumo equations on cylindrical surfaces ⋮ Existence of Periodic Solutions of the FitzHugh--Nagumo Equations for an Explicit Range of the Small Parameter ⋮ Inhibitor-induced wavetrains and spiral waves in an extended FitzHugh-Nagumo model of nerve cell dynamics ⋮ Theory of periodic and solitary space charge waves in extrinsic semiconductors ⋮ Rotating spiral waves in excitable media: the analytical results

Cites Work

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• Neutrally stable traveling wave solutions of nerve conduction equations
• A geometric approach to singular perturbation problems with applications to nerve impulse equations
• Stability of periodic travelling wave solutions of a nerve conduction equation
• THE EXISTENCE OF PERIODIC SOLUTIONS TO NAGUMO'S EQUATION
• ON THE EXISTENCE OF HOMOCLINIC AND PERIODIC ORBITS FOR THE FITZHUGH-NAGUMO EQUATIONS

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