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Title of Journal: Nonlinear Dyn

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Abbravation: Nonlinear Dynamics

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Springer Netherlands

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10.1016/j.annfar.2014.07.196

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1573-269X

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Dynamics in two nonsmooth predator–prey models wit

Authors: Yunfei Lv Rong Yuan Yongzhen Pei
Publish Date: 2013/05/23
Volume: 74, Issue: 1-2, Pages: 107-132
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Abstract

Considering a good pest control program should reduce the pest to levels acceptable to the public we investigate the threshold harvesting policy on pests in two predator–prey models Both models are nonsmooth and the aim of this paper is to provide how threshold harvesting affects the dynamics of the two systems When the harvesting threshold is larger than some positive level the harvesting does not affect the ecosystem when the harvesting threshold is less than the level the model has complex dynamics with multiple coexistence equilibria limit cycle bistability homoclinic orbit saddlenode bifurcation transcritical bifurcation subcritical and supercritical Hopf bifurcation Bogdanov–Takens bifurcation and discontinuous Hopf bifurcation Firstly we provide the complete stability analysis and bifurcation analysis for the two models Furthermore some numerical simulations are given to illustrate our results Finally it is found that harvesting lowers the level of both species for natural enemy–pest system while raises the densities of both species for the pest–crop system It is seen that the threshold harvesting policy of the enemy system is more effective than the crop systemWe are extremely grateful to the critical comments and invaluable suggestions made by anonymous honorable reviewers This work is supported by the Natural Science Foundation of China the Doctoral Program of Higher Education of China and National Natural Science Foundation of China 11101305

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