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Hopf bifurcation analysis on general Gause-type predator-prey models with delay. (English) Zbl 1246.37095
A class of three-dimensional Gause-type predator-prey models with delay is considered. Firstly, some sufficient conditions for the existence of a Hopf bifurcation are obtained by employing the polynomial theorem and analyzing the distribution of the roots of the associated characteristic equation. Secondly, the direction of the Hopf bifurcation and the stability of the bifurcated periodic solutions are determined by applying the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the obtained results.
MSC:
37N25Dynamical systems in biology
92B05General biology and biomathematics
35B32Bifurcation (PDE)
37G15Bifurcations of limit cycles and periodic orbits