Stability Property of a Predator-Prey System with a Constant Proportion of Prey Refuge and Stage-Structure for Prey Species

A predator-prey system with a constant proportion of prey refuge and stage-structure for prey species is proposed and studied in this paper. A set of conditions for the permanence of the system is obtained. The local stability of the system is discussed by the sign of eigenvalues. Furthermore, by using the iterative method, some suitable sufficient conditions for the global attractivity of the interior equilibrium is obtained. Our study shows that the constant proportion of prey refuge could lead to more complicated dynamic behaviors. Numerical simulations are also presented to illustrate the feasibility of the main results.