Global Stability for a Generalized Predator—Prey System with Time Delay In Two-patch Environments

Abstract

In this article the asymptotic behavior of solutions of a predator—prey system is investigated. The model incorporates time delay due to gestation and assumes that the prey disperses between two patches of a heterogeneous environment with barriers between patches and that the predator disperses between the patches with no barrier. Conditions are derived for the global asymptotic stability of a positive equilibrium.

Keywords:

• Global stability
• Delay
• Lyapunov functional

AMS Subject Classiflcations:

• 34D23
• 34K20
• 92D25