Ionic channel density of excitable membranes can act as a bifurcation parameter

DOI10.1007/BF00335156zbMath0466.92007WikidataQ52749310 ScholiaQ52749310MaRDI QIDQ1155525

S. H. Smith

Publication date: 1981

Published in: Biological Cybernetics (Search for Journal in Brave)

zbMATH Keywords

Hopf bifurcationHodgkin-Huxley equationsexcitable membranesionic channel density

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) Physiological, cellular and medical topics (92Cxx)

Related Items (7)

Analysis of the effects of modulatory agents on a modeled bursting neuron: Dynamic interactions between voltage in calcium dependent systems ⋮ The singularly perturbed Hodgkin-Huxley equations as a tool for the analysis of repetitive nerve activity ⋮ Bistability at the onset of neuronal oscillations ⋮ Partition of the Hodgkin-Huxley type model parameter space into the regions of qualitatively different solutions ⋮ Coupling of a slow and a fast oscillator can generate bursting ⋮ Random currents through nerve membranes. I. Uniform Poisson or white noise current in one-dimensional cables ⋮ On the reversible and irreversible representations of motions in \(R^ n\) to \(R^ 2\)

Cites Work

• Numerical calculation of stable and unstable periodic solutions to the Hodgkin-Huxley equations
• Autorhythmicity and entrainment in excitable membranes
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• 23.—Oscillation Phenomena in the Hodgkin-Huxley Equations
• The bifurcation of periodic solutions in the Hodgkin-Huxley equations

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