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An Application of Filippov Systems to Model Discontinuous Harvesting in a Predator-Prey Model

Norden, Janis (2018) An Application of Filippov Systems to Model Discontinuous Harvesting in a Predator-Prey Model. Bachelor's Thesis, Mathematics.


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Harvesting of the predators is introduced to a Rosenzweig-MacArthur predator-prey model whenever the population density of the predators exceeds a certain threshold value. This introduces a discontinuity along the threshold value in the vector field describing the dynamics. A continuous version of the Rosenzweig-MacArthur model is discussed in detail. It follows an introduction to the theory of Filippov systems and discontinuity-induced bifurcations. These are bifurcations that arise due to interactions with the line of discontinuity in the vector field. Finally, the theory is applied to the case of a one parameter family of Filippov systems which is based on the Rosenzweig-MacArthur model and describes the population-density-dependent harvesting. It is found that due to interactions with the discontinuity line, there exist parameter intervals where there are two attractors. This is a significant change in the behaviour of solutions to this system since the continuous version of the predator-prey model only allows for a single attractor at all times. It is concluded that population-density-dependent harvesting could be used to stabilize sensible ecosystems that exhibit potentially dangerous excursions of periodic solutions which come close to the coordinate axes.

Item Type: Thesis (Bachelor's Thesis)
Supervisor name: Waalkens, H. and Hoveijn, I.
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Date Deposited: 13 Jul 2018
Last Modified: 20 Jul 2018 12:33

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