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Zbl 1209.92058
Meng, Xin-You; Huo, Hai-Feng; Xiang, Hong
Hopf bifurcation in a three-species system with delays. (English)
[J] J. Appl. Math. Comput. 35, No. 1-2, 635-661 (2011). ISSN 1598-5865; ISSN 1865-2085/e

Summary: A kind of three-species system with Holling II functional response and two delays is introduced. Its local stability and the existence of Hopf bifurcation are demonstrated by analyzing the associated characteristic equation. By using the normal form method and center manifold theorem, explicit formulas to determine the direction of the Hopf bifurcation and the stability of bifurcating periodic solution are also obtained. In addition, the global existence results of periodic solutions bifurcating from Hopf bifurcations are established by using a global Hopf bifurcation result. Numerical simulation results are also given to support our theoretical predictions.

MSC 2000:: *92D40 Ecology
34K18 Bifurcation theory of functional differential equations
34K13 Periodic solutions of functional differential equations
34K20 Stability theory of functional-differential equations
65C60 Computational problems in statistics

Keywords: stability; Hopf bifurcation; delays; functional response

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