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We investigate the emergence of target waves in a cyclic predator-prey modelincorporating a periodic current of the three competing species in a small areasituated at the center of the square lattice. The periodic current acts as apacemaker, trying to impose its rhythm on the overall spatiotemporal evolutionof the three species. We show that the pacemaker is able to nucleate targetwaves that eventually spread across the whole population, whereby three routesleading to this phenomenon can be distinguished depending on the mobility ofthe three species and the oscillation period of the localized current. First,target waves can emerge due to the synchronization between the periodic currentand oscillations of the density of the three species on the spatial grid. Thesecond route is similar to the first, the difference being that thesynchronization sets in only intermittently. Finally, the third route towardstarget waves is realized when the frequency of the pacemaker is much higherthan that characterizing the oscillations of the overall density of the threespecies. By considering mobility and the frequency of the current as variableparameters, we thus provide insights into the mechanisms of pattern formationresulting from the interplay between local and global dynamics in systemsgoverned by cyclically competing species.

Emergence of target waves in paced populations of cyclically competing species