On predator invasion into a multi-patchy environment of two kinds of patches

We consider a Lotka-Volterra prey-predator two-species system in a n-patchy environment, assuming that predator can migrate among patches, while prey cannot. Those n patches are categorized into two groups, group 1 and group 2, according to the parameters determining the prey-predator relation and the predatorʹs migration process. Prey population in a patch of group 1 has parameters different from those for prey population in a patch of group 2. Predator population inhabiting and emigrating from a patch of group 1 has parameters different from those for predator population inhabiting and emigrating from a patch of group 2. Local stability of equilibrium states are analyzed, and the condition for the predatorʹs invasion success is derived to discuss the effect of environmentally heterogeneous patchiness on the coexistence of prey and predator.