Permanence and stability of a stage-structured predator-prey model

A predator-prey model with a stage structure for the predator which improve s the assumption that each individual predator has the same ability to capt ure prey is proposed. It is assumed that immature individuals and mature in dividuals of the predator are divided by a fixed age and that immature pred ators do not have the ability to attack prey. We obtain conditions that det ermine the permanence of the populations and the extinction of the populati ons. Furthermore, we establish necessary and sufficient conditions for the local stability of the positive equilibrium of the model. By exploiting the monotonicity of one equation of the model, we obtain conditions for the gl obal attractivity of the positive equilibrium, which allow for long delay a s long as the predator birth rate is large or the death rate of immature pr edators is small. By constructing Liapunov functionals, we also obtain cond itions under which the positive equilibrium is globally stable when the del ay is small. (C) 2001 Academic Press.