  The spontaneous generation of electrical activity underpins a number of
essential physiological processes, and is observed even in tissues where
specialized pacemaker cells have not been identified. The emergence of periodic
oscillations in diffusively coupled assemblies of excitable and electrically
passive cells (which are individually incapable of sustaining autonomous
activity) has been suggested as a possible mechanism underlying such phenomena.
In this paper we investigate the dynamics of such assemblies in more detail by
considering simple motifs of coupled electrically active and passive cells. The
resulting behavior encompasses a wide range of dynamical phenomena, including
chaos. However, embedding such assemblies in a lattice yields spatio-temporal
patterns that either correspond to a quiescent state or partial/globally
synchronized oscillations. The resulting reduction in dynamical complexity
suggests an emergent simplicity in the collective dynamics of such large,
spatially extended systems. Furthermore, we show that such patterns can be
reproduced by a reduced model comprising only excitatory and oscillatory
elements. Our results suggest a generalization of the mechanism by which
periodic activity can emerge in a heterogeneous system comprising
non-oscillatory elements by coupling them diffusively, provided their steady
states in isolation are sufficiently dissimilar.
