Bifurcation analysis of a delayed predator-prey model of prey migration and predator switching (Q2856976)

This paper analyzes the local stability of the positive equilibrium and the bifurcation of periodic solutions of a three-dimensional predator-prey model with two prey habitats, predator switching and delay due to predator gestation.NEWLINENEWLINEFirst, sufficient conditions for the local stability of the positive equilibrium regardless of the value of the delay and for the occurrence of Hopf bifurcation are found by linearizing the initial system and analyzing the roots of the associated characteristic equation, which is transcendental due to the presence of the delay. The direction of the Hopf bifurcation and the stability of the bifurcating periodic orbits are then determined by means of normal form theory and of the central manifold theorem. The above theoretical findings are also validated by means of numerical simulations.NEWLINENEWLINEAlthough the title of the paper describes the model as accounting for the effects of prey migration, it is to be noted that no explicit migration between prey habitats is accounted for (i.e., there are no explicit transfer terms between prey habitats), the effects of migration is implicitly described by means of predator switching.