Bifurcation analysis in a predator-prey system with time delay. (English) Zbl 1085.92052

Song, Yongli; Yuan, Sanling

Nonlinear Anal., Real World Appl. 7, No. 2, 265-284 (2006).

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:

92D40	Ecology
34K13	Periodic solutions to functional-differential equations
34K18	Bifurcation theory of functional-differential equations
37N25	Dynamical systems in biology
34K60	Qualitative investigation and simulation of models involving functional-differential equations

Keywords:

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

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