Volume 11, Number 1, Spring 2003
THE EFFECT OF COUPLING, NOISE, AND
HETEROGENEITY ON BURSTING
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.