Permanence of periodic Holling type predator-prey system with stage structure for prey

In this paper, we study the permanence of the following periodic Holling type predator-prey system with stage structure for preyx˙1(t)=a(t)x2(t)-b(t)x1(t)-d(t)x12(t)-e(t)x1γ(t)p(t)+x1γ(t)y(t),x˙2(t)=c(t)x1(t)-f(t)x22(t),y˙(t)=y(t)-g(t)+h(t)x1γ(t)p(t)+x1γ(t)-q(t)y(t).Sufficient and necessary condition which guarantee the predator and the prey species to be permanent is obtained. Some new results are obtained.