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Title: Glucose-induced period-doubling cascade in the electrical activity of pancreatic β-cells
Authors: Deng, B. 
Keywords: Asymptotic expansion
Bursting-spiking oscillations
Continuous spiking oscillations
Junction point
Junction-fold point
Kneading sequence
Period-doubling cascade
Poincaré map
Slow manifold
Stable and unstable foliations
Turning point
Issue Date: Jan-1999
Citation: Deng, B. (1999-01). Glucose-induced period-doubling cascade in the electrical activity of pancreatic β-cells. Journal of Mathematical Biology 38 (1) : 21-78. ScholarBank@NUS Repository.
Abstract: In the presence of stimulatory concentrations of glucose, the membrane potential of pancreatic β-cells may experience a transition from periods of rapid spike-like oscillations alternating with a pseudo-steady state to spike-only oscillations. Insulin secretion from β-cells closely correlates the periods of spike-like oscillations. The purpose of this paper is to study the mathematical structure which underlines this transitional stage in a pancreatic β-cell model. It is demonstrated that the transition can be chaotic but becomes more and more regular with increase in glucose. In particular, the system undergoes a reversed period-doubling cascade leading to the spike-only oscillations as the glucose concentration crosses a threshold. The transition interval in glucose concentration is estimated to be extremely small in terms of the rate of change for the calcium dynamics in the β-cells. The methods are based on the theory of unimodal maps and the geometric and asymptotic theories of singular perturbations. © Springer-Verlag 1999.
Source Title: Journal of Mathematical Biology
ISSN: 03036812
Appears in Collections:Staff Publications

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