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.
Highlights
Predator-prey interaction is one of the most important relationships in the ecosystem, so it has long been a focus of study in mathematical ecology
We prove the uniqueness of the order one periodic solution
We have proposed two predator-prey models with nonmonotonic functional response and state dependent impulsive harvesting
Summary
Predator-prey interaction is one of the most important relationships in the ecosystem, so it has long been a focus of study in mathematical ecology. If the prey exhibits group defense [1, 2], the predator growth rate will be inhibited when the prey density reaches a high level This phenomenon is known to exist widely in nature and considerable work on it has been studied [3,4,5,6,7,8]. We would better know some information about the amount of the species when we harvest them, we can avoid excessive exploitation and resource exhaustion To this end, we introduce a reliable real-time monitoring system to estimate the number of the species. The paper ends with a brief discussion and some numerical simulations
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