Persistence and global stability in a delayed predator-prey system with Holling-type functional response

Abstract

A delayed predator-prey system with Rolling type III functional response is investigated. It is proved that the system is uniformly persistent under some appropriate conditions. By means of suitable Lyapunov functionals, sufficient conditions are derived for the local and global asymptotic stability of a positive equilibrium of the system. Numerical simulations are presented to illustrate the feasibility of our main results. © Australian Mathematical Society 2004.