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Dynamics of a non‐selective harvesting predator–prey model with Hassell–Varley type functional response and impulsive effects
Author(s) -
Li Yaqin,
Huang Shoude,
Zhang Tianwei
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3468
Subject(s) - mathematics , functional response , type (biology) , fixed point theorem , complement (music) , fixed point , monotone polygon , comparison theorem , predation , mathematical analysis , predator , geometry , ecology , biology , biochemistry , chemistry , complementation , gene , phenotype
This paper is concerned with a non‐selective harvesting predator–prey model with Hassell–Varley type functional response and impulsive effects. By using the fixed point theory based on monotone operator, some simple conditions are obtained for the existence of at least one positive periodic solution of the model. The existence result of this paper implies that the functional response on prey does not influence the existence of positive periodic solution of the model, which completes some results given in recent years. Further, by applying the comparison theorem in impulsive differential equations and constructing a suitable Lyapunov functional, the permanence and global attractivity of the model are also investigated. The main results in this paper extend, complement, and improve the previously known result. And some examples and numerical simulations are given to illustrate the feasibility and effectiveness of the main results. Copyright © 2015 John Wiley & Sons, Ltd.