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Volume 11,     Number 1,     Spring 2003

 

THE EFFECT OF COUPLING, NOISE, AND HETEROGENEITY ON BURSTING OSCILLATIONS
GERDA DE VRIES

Abstract. Bursting refers to a complex oscillation characterized by a slow alternation between spiking behaviour and quiescence. In this paper, we give an overview of the bifurcation analysis of coupled models of square-wave bursting oscillations. The bifurcation analysis is facilitated by the decomposition of the system of equations into a fast and a slow subsystem. An investigation into the bifurcation structure of the fast subsystem reveals the different mechanisms underlying the modification of bursting characteristics by coupling itself and heterogeneity in the model parameters. Both weak and strong coupling regimes are discussed. Emergent bursting, that is, the genesis of bursting oscillations within a population of individuals that are incapable of bursting themselves, is reviewed as well. The bifurcation analysis reveals that emergent bursting is aided by heterogeneity or noise, depending on the strength of the coupling. Implications of the results obtained are discussed in the context of bursting oscillations observed in the membrane potential of pancreatic β-cells.

 

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