ISSN:
1432-1416
Keywords:
Key words: Bursting-spiking oscillations
;
Continuous spiking oscillations
;
Kneading sequence
;
Period-doubling cascade
;
Turning point
;
Junction point
;
Junction-fold point
;
Slow manifold
;
Stable and unstable foliations
;
Poincaré map
;
Asymptotic expansion
Source:
Springer Online Journal Archives 1860-2000
Topics:
Biology
,
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002850050141
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