Emerging spatio-temporal patterns in cyclic predator-prey systems with habitats

Cyclic predator prey systems are known to establish spiral waves that allow species to coexist. In this study, we analyze a structured heterogeneous system which gives one species an advantage to escape predation in an area, we refer to as a habitat, and study the effect on species coexistence and spatio-temporal patterns. We analyze the density of each species after giving one species a higher escape rate in a rock-paper-scissors game and find the species given the advantage carries the largest population as long as the escape rate assigned is below a threshold. After this threshold is exceeded, the species with the largest population is, instead, the predator of the species with the advantage. Numerical analysis of the spatial density of each species, as well as the analysis of a two-point correlation function for both inside and outside the habitats point to the same results. We also extend the analysis to a six species game that exhibits spontaneous spiral waves.