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

In this paper, we study the permanence of the following periodic Holling type-IV predator–prey system with stage structure for prey ẋ1(t)=a(t)x2(t)−b(t)x1(t)−d(t)x12(t)−p(t)x1(t)k(t)+x12(t)y(t),ẋ2(t)=c(t)x1(t)−f(t)x22(t),ẏ(t)=y(t)(−g(t)+h(t)x1(t)k(t)+x12(t)−q(t)y(t)). Under certain assumptions, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained.