Behavioral refuges and predator-prey coexistence.

The effects of a behavioral refuge caused either by the predator optimal foraging or prey adaptive antipredator behavior on the Gause predator-prey model are studied. It is shown that both of these mechanisms promote predator-prey coexistence either at an equilibrium, or along a limit cycle. Adaptive prey refuge use leads to hysteresis in prey antipredator behavior which allows predator-prey coexistence along a limit cycle. Similarly, optimal predator foraging leads to sigmoidal functional responses with a potential to stabilize predator-prey population dynamics at an equilibrium, or along a limit cycle.