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 rateβas control parameter. Besides, we also study the homoclinic bifurcation of the second system about parameterδon the basis of the theory of rotated vector field. Finally, numerical simulations are presented to illustrate the results.
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