Effects of a pestilent species on the stability of cyclically dominant species

Cyclic dominance is frequently believed to be a mechanism that maintains diversity of competing species. But this delicate balance could also fragile if some the members weakened because an extinction species will involve annihilation its predator hence leaving only single alive. To check expectation we here introduce fourth which chases exclusively member basic model composed by three cyclically dominant Interestingly, coexistence not necessarily broken and have detected consecutive phase transitions as vary invasion strength pestilent The resulting phases are analyzed different techniques including study Hamming distance density profiles. Some our observations strengthen previous findings about system, but they offer new revelations counter-intuitive phenomenon, like supporting may result in extinction, enriching understanding these very simple still surprisingly complex systems.