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Global analysis in a predator-prey system with nonmonotonic functional response. (English) Zbl 0986.34045
Here, the authors investigate a predator-prey system with a nonmonotonic functional response. In the first part of the paper, they investigate the global asymptotic behavior of the system. More precisely, they give conditions for the global stability of the interior equilibrium. They prove an existence result for limit cycles and their uniqueness. They obtain sub and super critical Hopf bifurcation. Also they prove that a limit cycle and homoclinic loop can not coexist. Finally, they give a classification of the asymptotic behavior depending on the parameter values of the system.
The second part of the paper is devoted to the Bogdanov-Takens bifurcation. More precisely, they first use a (nontrivial) transformation of the system. After this transformation, they derive a small perturbation of a new system for which the Bogdanov-Takens bifurcation was already studied.
Reviewer: P.Magal (Le Havre)

MSC:
34D23 Global stability of solutions to ordinary differential equations
92D25 Population dynamics (general)
34C25 Periodic solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
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