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Bifurcations in predator-prey systems with nonmonotonic functional response. (English) Zbl 1089.34060

The authors are concerned with predator-prey equations with delays, where the delay is considered as a bifurcation parameter. The paper begins by reviewing existing published results in the case, where there is no delay, for example. This provides the basis for the new results. The authors show that Hopf bifurcations arise at a sequence of delays \(\{\tau_k\}\) and they study the stability of the bifurcating nontrivial periodic solutions. In the final section of the paper, it is shown that for all positive delays, the system has a Bogdanov-Takens singularity.

MSC:

34K18 Bifurcation theory of functional-differential equations
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
34K60 Qualitative investigation and simulation of models involving functional-differential equations
92D25 Population dynamics (general)
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