  Reaction-diffusion (RD) mechanisms in chemical and biological systems can
yield a variety of patterns that may be functionally important. We show that
diffusive coupling through the inactivating component in a generic model of
coupled relaxation oscillators give rise to a wide range of spatio-temporal
phenomena. Apart from analytically explaining the genesis of anti-phase
synchronization and spatially patterned oscillatory death regimes in the model
system, we report the existence of a chimera state, characterized by spatial
co-occurrence of patches with distinct dynamics. We also observe propagating
phase defects in both one- and two-dimensional media resembling persistent
structures in cellular automata, whose interactions may be used for computation
in RD systems.
