The effects of the intensity of coupling and the time delay on the pro
perties of circulating spatiotemporal firing patterns in several simpl
e cell arrays have been studied for the Belousov-Zhabotinskii (BZ) and
chlorine dioxide-iodide reaction kinetics models. Single firing and f
inite cascade of firings have been found for both systems, but permane
nt firing has been observed only in the Oregonator model of the BZ rea
ction. The existence of regimes with permanent firing have been explai
ned on the basis of the difference in the course of concentration traj
ectories of the studied systems.