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Zhang, Jianming; Zhang, Lijun; Khalique, Chaudry Masood

Stability and Hopf bifurcation analysis on a Bazykin model with delay. (English) Zbl 1406.92538

Abstr. Appl. Anal. 2014, Article ID 539684, 7 p. (2014).
Summary: The dynamics of a prey-predator system with a finite delay is investigated. We show that a sequence of Hopf bifurcations occurs at the positive equilibrium as the delay increases. By using the theory of normal form and center manifold, explicit expressions for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived.

Cited in 1 Document

MSC:

92D25 Population dynamics (general)
34C23 Bifurcation theory for ordinary differential equations

Keywords:

predator-prey Bazykin model; stability; Hopf bifurcation
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References:

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