Periodic Solutions and Homoclinic Bifurcations of Two Predator-Prey Systems with Nonmonotonic Functional Response and Impulsive Harvesting

Abstract

Two predator-prey models with nonmonotonic functional response and state-dependent impulsive harvesting are formulated and analyzed. By using the geometry theory of semicontinuous dynamic system, we obtain the existence, uniqueness, and stability of the periodic solution and analyse the dynamic phenomenon of homoclinic bifurcation of the first system by choosing the harvesting rate $\beta$ as control parameter. Besides, we also study the homoclinic bifurcation of the second system about parameter $\delta$ on the basis of the theory of rotated vector field. Finally, numerical simulations are presented to illustrate the results.