An age-structured model of cannibalism

Abstract

We investigate the predator-prey model with cannibalism in the predator population, suggested by Magnusson [5] in 1995. We explore the model by a theory of bifurcations, based mainly on the results of Bautin. Among others, we show that the limit cycle appearing in the model due to the Andronov-Hopf bifurcation may be stable or unstable.

Keywords

• Cannibalism
• predator-prey
• Hopf bifurcation
• Lyapunov coefficient.