*(English)*Zbl 0945.92021

Summary: The influence of optimal antipredator behavior of prey on predator-prey dynamics in a two-patch environment is studied. One patch represents an open habitat while the other is a refuge for prey. It is assumed that prey maximize their fitness measured by the instantaneous per capita growth rate. In each patch population dynamics is described by the Lotka-Volterra time continuous model. The refuge is characterized by its protectiveness which is inversely related to the predation risk for prey, and the dependence of population dynamics on protectiveness is studied.

It is shown that adaptive behavior of prey changes qualitative properties of the underlying Lotka-Volterra model due to the appearance of a bounded attractor. Adaptive prey behavior does not lead to a stable equilibrium but to the reduction of population fluctuations. Dynamic consequences of a limited carrying capacity of the refuge are also considered. Low refuge carrying capacity leads to stability of predator-prey dynamics while stability is lost when the carrying capacity of the refuge is high. Lastly, it is shown that optimal antipredator behavior of prey leads to persistence and reduction of oscillations in population densities.