Dynamic behaviors of a nonautonomous predator–prey system with Holling type II schemes and a prey refuge

Abstract

Abstract In this paper, we consider a nonautonomous predator–prey model with Holling type II schemes and a prey refuge. By applying the comparison theorem of differential equations and constructing a suitable Lyapunov function, sufficient conditions that guarantee the permanence and global stability of the system are obtained. By applying the oscillation theory and the comparison theorem of differential equations, a set of sufficient conditions that guarantee the extinction of the predator of the system is obtained.

Keywords

• Predator–prey
• Permanence
• Holling type II
• Global stability
• Refuge