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Mathematical Biology Seminar - Gail Wolkowicz - Predator-Prey and Host-Parasitoid Dynamics: A Bifurcation Theory Approach

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HH/410

Speaker: Gail Wolkowicz (McMaster University)

Title: Predator-Prey and Host-Parasitoid Dynamics: A Bifurcation Theory Approach

Abstract: PART I: Sensitivity of the General Rosenzweig--MacArthur Model to the Mathematical Form of the Functional Response

The Rosenzweig--MacArthur predator-prey model has been shown to be sensitive to the mathematical form used to model the predator response function even if the forms have the same basic shape: zero at zero, monotone increasing, concave down, and saturating. This model is revisited to help explain this sensitivity in the case of Holling type II: Monod , Ivlev, and hyperbolic trigonometric response functions. Local and global dynamics are considered and the possible bifurcations with respect to variation of the carrying capacity of the prey, a measure of the enrichment of the environment are determined.

PART II: Pest Control by Generalist Parasitoids

A model studied by Magal, Cosner, and Ruan (Math. Med.Biol. 25,1-20; 2008) concerning host-parasitoid dynamics was motivated by the need for biological control of horse-chestnut leaf miners that spread through Europe.  A case missed in their investigation and the ramifications for possible pest control strategies are considered using a bifurcation theory approach.

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