Traveling waves of infinitely many pulses in nerve equations

DOI10.1016/0025-5564(81)90095-XzbMath0476.92008MaRDI QIDQ1160093

John A. Feroe

Publication date: 1981

Published in: Mathematical Biosciences (Search for Journal in Brave)

zbMATH Keywords

periodic solutionsHeaviside step functionFitzhugh nerve axon equationpiecewise linear FitzHugh-Nagumo equations

Mathematics Subject Classification ID

Periodic solutions to PDEs (35B10) Initial-boundary value problems for second-order parabolic equations (35K20) Parabolic equations and parabolic systems (35K99) Physiological, cellular and medical topics (92Cxx)

Related Items (9)

Traveling waves in lattice models of multidimensional and multicomponent media. II. Ergodic properties and dimension ⋮ A threshold for a caricature of the nerve equation ⋮ EVANS FUNCTIONS AND BIFURCATIONS OF STANDING WAVE FRONTS OF A NONLINEAR SYSTEM OF REACTION DIFFUSION EQUATIONS ⋮ Heteroclinic waves of the FitzHugh-Nagumo equations ⋮ HOMOCLINIC BRANCH SWITCHING: A NUMERICAL IMPLEMENTATION OF LIN'S METHOD ⋮ Evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations ⋮ Traveling waves in the Baer and Rinzel model of spine studded dendritic tissue ⋮ Unnamed Item ⋮ Existence of homoclinic connections in continuous piecewise linear systems

Cites Work

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• A geometric approach to singular perturbation problems with applications to nerve impulse equations
• Nagumo's equation
• Automatic Computation of Nerve Excitation—Detailed Corrections and Additions
• Double Impulse Solutions in Nerve Axon Equations
• Existence and Stability of Multiple Impulse Solutions of a Nerve Equation
• THE EXISTENCE OF PERIODIC SOLUTIONS TO NAGUMO'S EQUATION
• ON THE EXISTENCE OF HOMOCLINIC AND PERIODIC ORBITS FOR THE FITZHUGH-NAGUMO EQUATIONS
• Perturbation analysis of an approximation to the Hodgkin-Huxley theory
• A CONTRIBUTION TO THE PROBLEM OF THE STRUCTURE OF AN EXTENDED NEIGHBORHOOD OF A ROUGH EQUILIBRIUM STATE OF SADDLE-FOCUS TYPE

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