Permanence and existence of periodic solution of a discrete periodic Lotka–Volterra competition system with feedback control and time delays

Abstract

In this paper, we consider a discrete predator–prey system with feedback and time delays. By applying the theory of difference inequality, as well as analysis technique, sufficient conditions are obtained for the permanence of the system. And by applying Mawhin's coincidence degree theory, we obtain the existence of the positive periodic solutions.

Keywords

• discrete competition system
• permanence
• periodic solution
• feedback control
• coincidence degree theory