This study examines the influence of individual behavior on predator-prey dynamics in a two-patch environment. I assume that individuals behave to maximize their fitness measured by the instantaneous per capita growth rate. The population dynamics in each patch are described by the Lotka-Volterra continuous model. Two cases are studied in detail. The first case assumes only predators are free to move between patches, whereas the second assumes that both predators and prey move freely between patches. The study shows that the optimal behavior of animals leads to persistence of predator-prey systems and reduction of oscillations in population densities.