  Pancreatic islets, controlling glucose homeostasis, consist of \alpha, \beta,
and \delta\ cells. It has been observed that \alpha\ and \beta\ cells generate
out-of-phase synchronization in the release of glucagon and insulin,
counter-regulatory hormones for increasing and decreasing glucose levels, while
\beta\ and \delta\ cells produce in-phase synchronization in the release of the
insulin and somatostatin. Pieces of interactions between the islet cells have
been observed for a long time, although their physiological role as a whole has
not been explored yet. We model the synchronized hormone pulses of islets with
coupled phase oscillators that incorporate the observed cellular interactions.
The integrated model shows that the interaction from \beta\ to \delta\ cells,
of which sign has controversial reports, should be positive to reproduce the
in-phase synchronization between \beta\ and \delta\ cells. The model also
suggests that \delta\ cells help the islet system flexibly respond to changes
of glucose environment.
