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Hopf bifurcation of a ratio-dependent predator-prey system with time delay. (English) Zbl 1198.34149

Summary: We consider a ratio dependent predator-prey system with time delay where the dynamics is logistic with the carrying capacity proportional to prey population. By considering the time delay as bifurcation parameter, we analyze the stability and the Hopf bifurcation of the system based on the normal form approach and the center manifold theory. Finally, we illustrate our theoretical results by numerical simulations.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:

34K18 Bifurcation theory of functional-differential equations
37N25 Dynamical systems in biology
92D25 Population dynamics (general)
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