An application of Conley index techniques to a model of bursting in excitable membranes

DOI10.1006/jdeq.1999.3686zbMath0958.34037OpenAlexW2076332824MaRDI QIDQ1566848

William M. Kinney

Publication date: 28 September 2000

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.1999.3686

zbMATH Keywords

singular perturbationattractorConley indexHodgkin-Huxley modelfast-slow systemisolating neighborhood

Mathematics Subject Classification ID

Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Biomechanics (92C10) Singular perturbations of ordinary differential equations (34D15) Cell biology (92C37) Attractors of solutions to ordinary differential equations (34D45) Index theory for dynamical systems, Morse-Conley indices (37B30) Singular perturbations for ordinary differential equations (34E15) Cell movement (chemotaxis, etc.) (92C17)

Related Items (3)

Symmetric bursting behaviors in the generalized FitzHugh-Nagumo model ⋮ Spike-adding canard explosion in a class of square-wave bursters ⋮ Applying the Conley index to fast-slow systems with one slow variable and an attractor

Cites Work

• Chaos in a three-variable model of an excitable cell
• A geometric approach to singular perturbation problems with applications to nerve impulse equations
• Singular index pairs
• The transition from bursting to continuous spiking in excitable membrane models
• Zeta functions, periodic trajectories, and the Conley index
• Chaotic Spikes Arising from a Model of Bursting in Excitable Membranes
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