Birth Rate Effects on an Age-Structured Predator-Prey Model with Cannibalism in the Prey

Abstract

We develop a family of predator-prey models with age structure and cannibalism in the prey population. It consists of systems of $m$ ordinary differential equations, where $m$ is a parameter associated with new proposed prey birth rates. We discuss how these new birth rates give the required flexibility to produce differential systems with well-behaved solutions. The main feature required in these models is the coexistence among the involved species, which translates mathematically into stable equilibria and periodic solutions. The search for such characteristics is based on heuristic predation functions that account for cannibalism in the prey.