Cannibalism in an age-structured predator–prey system

The effect of cannibalism on an age-structured predator–prey system is studied. Three stable equilibrium states are found. Using a Hopf bifurcation analysis, it is found that the non washout steady state looses its stability as the cannibalism attack rate increases past a bifurcation point Sc. The dependence of the bifurcation point on the other parameters in the model is found. It is shown that the trajectory of the solution spirals in for attack rates S<Sc and exhibits limit cycle behavior for S>Sc.