Periodic solutions for generalized predator-prey systems with time delay and diffusion

A set of easily verifiable sufficient conditions axe derived for the existence of positive periodic solutions for delayed generalized predator-prey dispersion system x(1)'(t) = x(1)(t)g(1)(t, x(1) (t)) - a1(t)y(t)p(1)(x(1)(t)) + D-1(t)(x(2)(t) - x(1)(t)), x(2)'(t) = x(2)(t)g(2)(t,w(2)(t)) - a(2)(t)y(t)p(2)(x(2)(t)) + D-2(t)(x(1)(t) - x(2)(t)), y'(t) = y(t)[-h(t, y(t)) + b(1)(t)p(1)(x(1)(t - r(1))) + b(2)(t)p(2)(x(2)(t - r(2)))], where a(i)(t), b(i)(t) and D-i(t)(i = 1, 2) are positive continuous T-periodic functions, g(i)(t, x(i)) (i = 1, 2) and h(t, y) are continuous and T-periodic with respect to t and h(t, y) > 0 for y > 0, t, y E R(i)p(i) (x) (i = 1, 2) are continuous and monotonously increasing functions, and p(i)(x(i)) > 0 for x(i) > 0.