  In shear flows like pipe flow and plane Couette flow there is an extended
range of parameters where linearly stable laminar flow coexists with a
transient turbulent dynamics. When increasing the amplitude of a perturbation
on top of the laminar flow, one notes a a qualitative change in its lifetime,
from smoothly varying and short one on the laminar side to sensitively
dependent on initial conditions and long on the turbulent side. The point of
transition defines a point on the edge of chaos. Since it is defined via the
lifetimes, the edge of chaos can also be used in situations when the turbulence
is not persistent. It then generalises the concept of basin boundaries, which
separate two coexisting attractors, to cases where the dynamics on one side
shows transient chaos and almost all trajectories eventually end up on the
other side. In this paper we analyse a two-dimensional map which captures many
of the features identified in laboratory experiments and direct numerical
simulations of hydrodynamic flows. The analysis of the map shows that different
dynamical situations in the edge of chaos can be combined with different
dynamical situations in the turbulent region. Consequently, the model can be
used to develop and test further characterisations that are also applicable to
realistic flows.
