Global attractivity of a nonautonomous Lotka–Volterra predator–prey model in a two-patch environment

This study proposes a novel mathematical model of an ecosystem in which two patches are inhabited by the same species of prey and predator. The prey in each patch move between patches to avoid predator attacks, whereas the predators do not move between patches because of factors such as their habits, reproductive behavior, and territories. Additionally, the study focuses on the asymptotic behavior of the population (or population density) of the four species; in particular, a set of populations remains in a four-dimensional bounded region and eventually converges to a specific interior point within that bounded region. Ecosystems are constantly affected by both natural and anthropogenic (human-induced) disturbances. The proposed ecosystem model is described by a system of differential equations with time-varying coefficients in addition to constant coefficients to incorporate the effects of disturbances. If the set of populations always converges to the same interior point regardless of the initial data, then the four species will coexist, that is, the model is permanent. Thus, this result demonstrates that the model is permanent under specific assumptions.