Hopf bifurcation and chaos control for a Leslie–Gower type generalist predator model

This paper is concerned with chaos control and bifurcations of the Leslie–Gower type generalist predator model in a tri-trophic food web system with the time-delayed feedback control. First, the distribution of the roots of the related characteristic equations is analyzed by the polynomial theorem, the conditions to guarantee the existence of Hopf bifurcation are given by choosing the time delay as a bifurcation parameter. Then, the explicit formula for direction of Hopf bifurcation and stability of periodic solutions bifurcating are determined by using the normal form theory and center manifold theorem. Finally, the correctness of our theoretical analysis is verified by some numerical simulation.