  While interdependent systems have usually been associated with increased
fragility, we show that strengthening the interdependence between dynamical
processes on different networks can make them more robust. By coupling the
dynamics of networks that in isolation exhibit catastrophic collapse with
extinction of nodal activity, we demonstrate system-wide persistence of
activity for an optimal range of interdependence between the networks. This is
related to the appearance of attractors of the global dynamics comprising
disjoint sets ("islands") of stable activity.
