Uniform persistence and periodic solutions for a discrete predator–prey system with delays ✩

In this paper, we deal with a discrete predator–prey system with delay. We first give a sufficient condition for the uniform persistence of the system. Assuming that the coefficients in the system are periodic, by generalizing the Yoshizawa’s theorem on the existence of periodic solution for ordinary differential equations to the difference equations with delays, we obtain the existence of a periodic solution basing on the uniform persistence result.  2005 Elsevier Inc. All rights reserved.