HOPF BIFURCATION ANALYSIS FOR A DELAYED PREDATOR-PREY SYSTEM WITH A PREY REFUGE AND SELECTIVE HARVESTING | Zendy

Miao Peng | Zendy; Zhengdi Zhang | Zendy; Xuedi Wang | Zendy; Xiuyu Liu | Zendy

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HOPF BIFURCATION ANALYSIS FOR A DELAYED PREDATOR-PREY SYSTEM WITH A PREY REFUGE AND SELECTIVE HARVESTING

Author(s) -

Miao Peng,

Zhengdi Zhang,

Xuedi Wang,

Xiuyu Liu

Publication year - 2018

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2018.982

Subject(s) - center manifold , hopf bifurcation , mathematics , functional response , predation , control theory (sociology) , bifurcation , saddle node bifurcation , stability (learning theory) , transcritical bifurcation , mathematical analysis , predator , nonlinear system , ecology , physics , computer science , biology , control (management) , quantum mechanics , artificial intelligence , machine learning

In this paper, a delayed predator-prey system with Holling type III functional response incorporating a prey refuge and selective harvesting is considered. By analyzing the corresponding characteristic equations, the conditions for the local stability and existence of Hopf bifurcation for the system are obtained, respectively. By utilizing normal form method and center manifold theorem, the explicit formulas which determine the direction of Hopf bifurcation and the stability of bifurcating period solutions are derived. Finally, numerical simulations supporting the theoretical analysis are given.

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