Propagation and Its Failure in Coupled Systems of Discrete Excitable Cells

1987/06/01 by James P. Keener · 8 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Medicine · #Gene Regulatory Network Analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation

paper · doi:10.1137/0147038

crossref issued 1987/06/01 · crossref published 1987/06/01 · crossref published-print 1987/06/01 · openalex publication_date 1987/06/01 · crossref created 2005/02/23 · crossref deposited 2017/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/23 · crossref indexed 2026/07/31

Abstract

We study propagation and its failure in systems of discrete coupled excitable cells. It is shown that propagation fails when coupling is weak, but succeeds if coupling is strong enough. We use a theorem of Moser on maps of the plane to establish the existence of an infinite variety of stable standing solutions when coupling is small. We use upper and lower solution techniques and perturbation analysis to show that propagation is successful when the coupling strength is large enough. These results are applied to the cubic FitzHugh–Nagumo dynamics as well as to the more realistic Beeler–Reuter model of action potentials in myocardial cells.

Citations

• A quantitative description of membrane current and its application to conduction and excitation in nerve
• Impulses and Physiological States in Theoretical Models of Nerve Membrane
• Numerical solution of a nonlinear advance-delay-differential equation from nerve conduction theory

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