Journal Article

Detection of slow-fast limit cycles in a model for electrical activity in the pancreatic β-cell

YONGWIMON LENBURY, KANCHANA KUMNUNGKIT and BORIBOON NOVAPRATEEP

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 13, issue 1, pages 1-21
Published in print March 1996 | ISSN: 1477-8599
e-ISSN: 1477-8602 | DOI: http://dx.doi.org/10.1093/imammb/13.1.1
Detection of slow-fast limit cycles in a model for electrical activity in the pancreatic β-cell

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In this paper we consider a model for the phenomenon of bursting electrical activity in the pancreatic β-cell. Consisting of three coupled first-order nonlinear differential equations, the model describes the dynamics of the membrane potential, the activation parameter for the voltage-gated potassium channel, and the intracellular calcium concentration. The bursting electrical activity depends on fast and slow processes with distinctly different time scales which, when taken to the limit of highly diversified dynamics, allow the application of the singular perturbation method. Explicit conditions are derived which differentiate various dynamic behaviours and identify, in particular, the limit cycles composed of alternate slow and fast transitions. Computer simulations are then presented to support our theoretical predictions.

Keywords: limit cycles; singular perturbation; bursting activity; pancreas

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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