  A two-dimensional system of differential equations with delay modelling the
glucose-insulin interaction processes in the human body is considered.
Sufficient conditions are derived for the unique positive equilibrium in the
system to be globally asymptotically stable. They are given in terms of the
global attractivity of the fixed point in a limiting interval map. The
existence of slowly oscillating periodic solutions is shown in the case when
the equilibrium is unstable. The mathematical results are supported by
extensive numerical simulations. It is shown that typical behaviour in the
system is the convergence to either a stable periodic solution or to the unique
stable equilibrium. The coexistence of several periodic solutions together with
the stable equilibrium is demonstrated as a possibility.
