Global stability of a delayed nonlinear Lotka–Volterra system with feedback controls and patch structure

Abstract

In this paper, applying Lyapunov functional techniques to a nonlinear delayed Lotka–Volterra system with feedback controls and patch structure, we establish sufficient conditions of the global stability for a trivial equilibrium and a positive equilibrium, respectively. Moreover, we offer new techniques to prove the permanence and the existence of positive equilibrium of this system. The influence of the feedback controls can be essentially eliminated from the Lyapunov functional to prove the global stability, whereas feedback controls change the position of a unique positive equilibrium. These generalize the known results of recent literature.