Two types of predator-prey models with harvesting: Non-smooth and non-continuous

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:250

Article

Lv, Yunfei¹  Yuan, Rong¹  Pei, Yongzhen² 

[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Beijing 100875, Peoples R China

[2] Tianjin Polytech Univ, Sch Sci, Tianjin 300387, Peoples R China

关键词: Threshold harvesting;    Non-smooth;    Non-continuous;    Bogdanov-Takens bifurcation;    Discontinuous Hopf bifurcation;    Periodic solutions;   

DOI  :  10.1016/j.cam.2013.03.001

来源: Elsevier

【 摘 要 】

This article investigates continuous and impulsive threshold harvesting strategies on the predator which needs to be applied only when the predator population is above or reaches the harvesting threshold. For the continuous threshold model, the system is nonsmooth and has complex dynamics with multiple internal equilibria, limit cycle, homoclinic orbit, saddle-node bifurcation, transcritical bifurcation, subcritical and supercritical Hopf bifurcation, Bogdanov-Takens bifurcation and discontinuous Hopf bifurcation. In order to prevent the predator population being above the threshold, we further extend our model with impulsive threshold harvesting strategies. The model is non-continuous and the existence and stability of positive order-1 and order-2 periodic solutions were obtained by using the Poincare map. It is seen that the impulsive threshold harvesting strategies are more effective than the continuous. Furthermore, some numerical simulations are given to illustrate our results. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free