Computer-aided experiments on the Hopf bifurcation of the FitzHugh-Nagumo nerve model

DOI10.1016/0898-1221(95)00041-VzbMath0820.92003OpenAlexW2018004271MaRDI QIDQ1894192

Mo-Hong Chou

Publication date: 14 September 1995

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(95)00041-v

zbMATH Keywords

hysteresisperiodic solutionsHopf bifurcationcritical pointsrelaxation oscillationmultiple steady statescusp formationperiod diagramspace-clamped FitzHugh-Nagumo nerve model

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Neural biology (92C20) Bifurcation theory for ordinary differential equations (34C23) Numerical investigation of stability of solutions to ordinary differential equations (65L07) Numerical methods for ordinary differential equations (65L99)

Related Items (4)

OREGONATOR-BASED SIMULATION OF THE BELOUSOV–ZHABOTINSKII REACTION ⋮ Exotic dynamic behavior of the forced FitzHugh-Nagumo equations ⋮ Zero-Hopf bifurcation in the FitzHugh-Nagumo system ⋮ Qualitative analysis of bounded traveling wave solutions to Nagumo nerve conduction equation and its approximate oscillatory solutions

Uses Software

• Mathematica
• AUTO

Cites Work

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• Perturbation methods, bifurcation theory and computer algebra
• Numerical methods in bifurcation problems. Lectures delivered at the Indian Institute of Science, Bangalore, under the T.I.F.R.-I.I.Sc. Programme in Applications of Mathematics. Notes by A. K. Nandakumaran and Mythily Ramaswamy
• Numerical calculation of stable and unstable periodic solutions to the Hodgkin-Huxley equations
• Hopf bifurcation in a reaction-diffusion system governed by the Fitz- Hugh-Nagumo equations
• A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides

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