  We describe an example of a structurally stable heteroclinic network for
which nearby orbits exhibit irregular but sustained switching between the
various sub-cycles in the network. The mechanism for switching is the presence
of spiralling due to complex eigenvalues in the flow linearised about one of
the equilibria common to all cycles in the network. We construct and use return
maps to investigate the asymptotic stability of the network, and show that
switching is ubiquitous near the network. Some of the unstable manifolds
involved in the network are two-dimensional; we develop a technique to account
for all trajectories on those manifolds. A simple numerical example illustrates
the rich dynamics that can result from the interplay between the various cycles
in the network.
