Asymptotic stability of linear and nonlinear model systems representing age-structured predator–prey interactions

We consider a predator–prey model system assuming predator population to be age-structured. This assumption works two-fold: (i) it facilitates consideration of predators' active involvement in predation to be predator age-dependent; (ii) it helps incorporate delay effects into the system. Our model formulation yields a nonlinear system of integro-differential equations of which the Sih model becomes a special case when all predators are assumed to be equally active in predation. We analyse both linear and nonlinear systems under fairly general conditions on functions and give sufficient conditions for asymptotic stability of the positive equilibrium solution of our model system. It is found that the advanced age-group predators' active involvement in predation promotes co-existence of species. This result seems to be against the usual rule of thumb that a large delay destabilizes the system. Finally, we emphasize that the stability results of this paper can be used in the study of prey-refuge effects on age-structured predator–prey interactions.