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Reaction-diffusion (RD) mechanisms in chemical and biological systems canyield a variety of patterns that may be functionally important. We show thatdiffusive coupling through the inactivating component in a generic model ofcoupled relaxation oscillators give rise to a wide range of spatio-temporalphenomena. Apart from analytically explaining the genesis of anti-phasesynchronization and spatially patterned oscillatory death regimes in the modelsystem, we report the existence of a chimera state, characterized by spatialco-occurrence of patches with distinct dynamics. We also observe propagatingphase defects in both one- and two-dimensional media resembling persistentstructures in cellular automata, whose interactions may be used for computationin RD systems.

Dynamical order, disorder and propagating defects in homogeneous system of relaxation oscillators