Stability and Hopf Bifurcation Analysis for a Gause-Type Predator-Prey System with Multiple Delays | Zendy

Juan Liu | Zendy; Changwei Sun | Zendy; Yimin Li | Zendy

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Stability and Hopf Bifurcation Analysis for a Gause-Type Predator-Prey System with Multiple Delays

Author(s) -

Juan Liu,

Changwei Sun,

Yimin Li

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 - 10.1155/2013/795358

Subject(s) - mathematics , hopf bifurcation , center manifold , pitchfork bifurcation , stability (learning theory) , type (biology) , saddle node bifurcation , transcritical bifurcation , bifurcation diagram , mathematical analysis , bifurcation , nonlinear system , ecology , physics , quantum mechanics , machine learning , computer science , biology

This paper is concerned with a Gause-type predator-prey system with two delays. Firstly,we study the stability and the existence of Hopf bifurcation at the coexistence equilibrium byanalyzing the distribution of the roots of the associated characteristic equation. A group ofsufficient conditions for the existence of Hopf bifurcation is obtained. Secondly, an explicitformula for determining the stability and the direction of periodic solutions that bifurcate fromHopf bifurcation is derived by using the normal form theory and center manifold argument. Finally, some numerical simulations are carried out to illustrate the main theoretical results

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