Persistence and Global Stability in a Delayed Gause-Type Predator Prey System without Dominating Instantaneous Negative Feedbacks

A delayed Gause-type predator prey system without dominating instantaneous negative feedbacks is investigated. It is proved that the system is uniformly persistent under some appropriate conditions. By means of constructing a suitable Lyapunov functional, sufficient conditions are derived for the local and global asymptotic stability of the positive equilibrium of the system