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Bogdanov-Takens bifurcation of a delayed ratio-dependent Holling-Tanner predator prey system. (English) Zbl 1470.34187

Summary: A delayed predator prey system with refuge and constant rate harvesting is discussed by applying the normal form theory of retarded functional differential equations introduced by Faria and Magalhães. The analysis results show that under some conditions the system has a Bogdanov-Takens singularity. A versal unfolding of the system at this singularity is obtained. Our main results illustrate that the delay has an important effect on the dynamical behaviors of the system.

MSC:

34K18 Bifurcation theory of functional-differential equations
92D25 Population dynamics (general)
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