The bifurcation of periodic solutions in the Hodgkin-Huxley equations
Open Access
- 1 April 1978
- journal article
- Published by American Mathematical Society (AMS) in Quarterly of Applied Mathematics
- Vol. 36 (1) , 73-83
- https://doi.org/10.1090/qam/472116
Abstract
We consider the current clamped version of the Hodgkin-Huxley nerve conduction equations. Under appropriate assumptions on the functions and parameters we show that there are two critical values of I I , the current parameter, at which a Hopf bifurcation of periodic orbits occurs.Keywords
This publication has 11 references indexed in Scilit:
- An applicable Hopf bifurcation formula and instability of small periodic solutions of the field-Noyes modelJournal of Mathematical Analysis and Applications, 1976
- On travelling wave solutions of the Hodgkin-Huxley equationsArchive for Rational Mechanics and Analysis, 1976
- Reconstruction of the electrical activity of cardiac Purkinje fibres.The Journal of Physiology, 1975
- Repetitive response of the Hodgkin-Huxley model for the squid giant axonJournal of Theoretical Biology, 1970
- The mechanism of oscillatory activity at low membrane potentials in cardiac Purkinje fibresThe Journal of Physiology, 1969
- Digital computer solutions for excitable membrane modelsJournal of Cellular and Comparative Physiology, 1965
- Thresholds and Plateaus in the Hodgkin-Huxley Nerve EquationsThe Journal of general physiology, 1960
- Automatic Computation of Nerve Excitation—Detailed Corrections and AdditionsJournal of the Society for Industrial and Applied Mathematics, 1959
- Automatic Computation of Nerve ExcitationJournal of the Society for Industrial and Applied Mathematics, 1955
- A quantitative description of membrane current and its application to conduction and excitation in nerveThe Journal of Physiology, 1952