Permanence and stability in non-autonomous predator–prey Lotka–Volterra systems with feedback controls

The main purpose of this article is considering whether or not the feedback controls have an influence on a non-autonomous predator–prey Lotka–Volterra type system. General criteria on permanence are established, which is described by an integral form and independent of some feedback controls. By constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for the global stability of any positive solution to the model.