Prey dominance in discrete predator-prey systems with a prey refuge

The effects of a prey refuge in a multiprey discrete system with predation is studied. We demonstrate the stable coexistence of species that would otherwise exclude each other without a prey refuge. With a prey refuge, we show that an endangered prey not only recovers from the brink of extinction, but also dominates the system. We invent notions of dominance that guarantee the extinction of all the dominated prey in the system. With the extermination of most of its prey, the predator either coexists with the dominant prey or is driven to extinction. By using a precise mathematical definition, we obtain that a prey with a sufficiently high carrying capacity persists in a predator-prey system with a prey refuge.