Global stability of a stage-structured predator-prey model with prey dispersal

A delayed Lotka–Volterra type predator-prey model with stage structure for predator and prey dispersal in two-patch environments is investigated. It is assumed that immature individuals and mature individuals of predator species are divided by a fixed age, and that immature predators do not feed on prey and do not have the ability to reproduce; on the other hand, it is assumed that the prey species can disperse between one patch with a low level of food and without predation and one patch with a higher level of food but with predation. By means of two different kinds of Lyapunov functionals, sufficient conditions are derived respectively for the global asymptotic stability of a positive equilibrium of the model. By analyzing the characteristic equation, criterion is established for the local stability of the positive equilibrium. Numerical simulations are presented to illustrate our main results.