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Zbl 1085.92052
Song, Yongli; Yuan, Sanling
Bifurcation analysis in a predator\,-\,prey system with time delay. (English)
[J] Nonlinear Anal., Real World Appl. 7, No. 2, 265-284 (2006). ISSN 1468-1218

Summary: A predator-prey system with a discrete delay and a distributed delay is investigated. We first consider the stability of the positive equilibrium and the existence of local Hopf bifurcations. In succession, using the normal form theory and a center manifold argument, we derive explicit formulas determining stability, direction and other properties of bifurcating periodic solutions. Finally, several numerical simulations for supporting the theoretical analysis are also given.

MSC 2000:: *92D40 Ecology
34K13 Periodic solutions of functional differential equations
34K18 Bifurcation theory of functional differential equations
37N25 Dynamical systems in biology
34K60 Applications of functional-differential equations

Keywords: Predator-prey system; Time delay; Stability; Hopf bifurcation; Periodic solutions

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