STABILITY AND HOPF BIFURCATION OF A MODIFIED DELAY PREDATOR-PREY MODEL WITH STAGE STRUCTURE | Zendy

Jing Li | Zendy; Shaotao Zhu | Zendy; Ruilan Tian | Zendy; Wei Zhang | Zendy; Xin Li | Zendy

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STABILITY AND HOPF BIFURCATION OF A MODIFIED DELAY PREDATOR-PREY MODEL WITH STAGE STRUCTURE

Author(s) -

Jing Li,

Shaotao Zhu,

Ruilan Tian,

Wei Zhang,

Xin Li

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 - 10.11948/2018.573

Subject(s) - hopf bifurcation , mathematics , period doubling bifurcation , saddle node bifurcation , bogdanov–takens bifurcation , transcritical bifurcation , predation , stability (learning theory) , control theory (sociology) , bifurcation , pitchfork bifurcation , mathematical analysis , equilibrium point , nonlinear system , physics , differential equation , ecology , economics , biology , computer science , control (management) , management , quantum mechanics , machine learning

In this paper, a modified delay predator-prey model with stage structure is established, which involves the economic factor and internal competition of all the prey and predator populations. By the methods of normal form and characteristic equation, we obtain the stability of the positive equilibrium point and the sufficient condition of the existence of Hopf bifurcation. We analyze the influence of the time delay on the equation and show the occurrence of Hopf bifurcation periodic solution. The simulation gives a visual understanding for the existence and direction of Hopf bifurcation of the model.

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