The Hopf Bifurcation for a Predator-Prey System with -Logistic Growth and Prey Refuge | Zendy

Shaoli Wang | Zendy; Zhihao Ge | Zendy

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The Hopf Bifurcation for a Predator-Prey System with -Logistic Growth and Prey Refuge

Author(s) -

Shaoli Wang,

Zhihao Ge

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/168340

Subject(s) - mathematics , center manifold , hopf bifurcation , logistic function , predation , transcritical bifurcation , saddle node bifurcation , pitchfork bifurcation , bifurcation , bifurcation diagram , ode , biological applications of bifurcation theory , mathematical analysis , statistics , nonlinear system , ecology , physics , quantum mechanics , biology

The Hopf bifurcation for a predator-prey system with -logistic growth and prey refuge is studied. It is shown that the ODEs undergo a Hopf bifurcation at the positive equilibrium when the prey refuge rate or the index- passed through some critical values. Time delay could be considered as a bifurcation parameter for DDEs, and using the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction of bifurcations and the stability and other properties of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main results

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