  We present a dynamical system that naturally exhibits two unstable attractors
that are completely enclosed by each others basin volume. This
counter-intuitive phenomenon occurs in networks of pulse-coupled oscillators
with delayed interactions. We analytically and numerically investigate this
phenomenon and clarify the mechanism underlying it: Upon continuously removing
the non-invertibility of the system, the set of two unstable attractors becomes
a set of two non-attracting saddle states that are heteroclinically connected
to each other. This transition from a network of unstable attractors to a
heteroclinic cycle constitutes a new type of bifurcation in dynamical systems.
