Invest conflicts of adult predators

Parental care is incorporated into a prey–predator model in which immature predators are taken care of by their parents. It is assumed that adult predators confront the problem to stay home to protect offspring or to go out to forage. The global dynamics of the mathematical model is analyzed by means of analytical methods and numerical simulations. Conditions for the extinction of predator populations are established and the manners in which predators become extinct are revealed. Bifurcation analysis shows that the model admits changes from the extinction of predators to stable coexistence at a positive equilibrium point, and then to stage-structure induced oscillations. It is shown that optimal invest of adult predators can be achieved.