Permanence of periodic Holling type predator-prey system with stage structure for prey
Abstract In this paper, we study the permanence of the following periodic Holling type predator–prey system with stage structure for prey x ˙ 1 ( t ) = a ( t ) x 2 ( t ) - b ( t ) x 1 ( t ) - d ( t ) x 1 2 ( t ) - e ( t ) x 1 γ ( t ) p ( t ) + x 1 γ ( t ) y ( t ) , x ˙ 2 ( t ) = c ( t ) x 1 ( t ) - f ( t ) x 2 2 ( t ) , y ˙ ( t ) = y ( t ) - g ( t ) + h ( t ) x 1 γ ( t ) p ( t ) + x 1 γ ( 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.