On the free boundary problem for a predator-prey model with fear effect

Abstract

This manuscript proposes a three-species model with a free food chain boundary to study the effects of fear. The well-posedness and uniform estimates for the solution are proved, as well as the behavior of the components of the solution and the unknown boundary over large time intervals. The findings suggest that the effect of fear of predators can move a system from a chaotic to a stable state. The results may provide useful biological information about ecosystems in which predator-prey interactions occur.