EXISTENCE OF PERIODIC SOLUTION AND PERSISTENCE FOR A DELAYED PREDATOR-PREY SYSTEM WITH DIFFUSION AND IMPULSE†

By using Mawhin continuation theorem and comparison theo- rem, the existence of periodic solution and persistence for a predator-prey system with diffusion and impulses are investigated in this paper. An example and simulation are given to show the effectiveness of the main results. x ' (t) = x1(t)(r1 − a11x1(t) − a12y(t)) + D21x2(t) − D12x1(t), x '(t) = −r2x2(t) + D12x1(t) − D21x2(t), y ' (t) = a31x1(t − τ )y(t − τ ) − ry(t) − a32y 2 (t),