  The dynamics of networks of interacting dynamical systems depend on the
nature of the coupling between individual units. We explore networks of
oscillatory units with coupling functions that have "dead zones", that is, the
coupling functions are zero on sets with interior. For such networks, it is
convenient to look at the effective interactions between units rather than the
(fixed) structural connectivity to understand the network dynamics. For
example, oscillators may effectively decouple in particular phase
configurations. Along trajectories the effective interactions are not
necessarily static, but the effective coupling may evolve in time. Here, we
formalize the concepts of dead zones and effective interactions. We elucidate
how the coupling function shapes the possible effective interaction schemes and
how they evolve in time.
