Phase transitions induced by variation of invasion rates in spatial   cyclic predator-prey models with four or six species
  Cyclic predator-prey models with four or six species are studied on a square lattice when the invasion rates are varied. It is found that the cyclic invasions maintain a self-organizing pattern as long as the deviation of the invasion rate(s) from a uniform value does not exceed a threshold value. For larger deviations the system exhibits a continuous phase transition into a frozen distribution of odd (or even) label species. 
Gyorgy Szabo and Attila Szolnoki