Global Dynamics of a Predator-prey Model with Stage Structure for Predator

The global properties of a predator-prey model with stage structure for predator are studied using Lyapunov functionals and LaSalle’s invariance principle. It is found that, under hypotheses which insure the uniform persistence of the system and the existence of a unique positive steady state, a feasible a-priori lower bound condition on the abundance of the prey population ensures the global asymptotic stability of the positive steady state. A condition which leads to the extinction of the predators is indicated. We also obtain results on the existence and stability of periodic solutions. The biological significance of the results is discussed.