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

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Abstract
Harvesting of the predators is introduced to a RosenzweigMacArthur predatorprey 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 RosenzweigMacArthur model is discussed in detail. It follows an introduction to the theory of Filippov systems and discontinuityinduced 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 RosenzweigMacArthur model and describes the populationdensitydependent 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 predatorprey model only allows for a single attractor at all times. It is concluded that populationdensitydependent 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)  

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Degree programme:  Mathematics  
Thesis type:  Bachelor's Thesis  
Date Deposited:  13 Jul 2018  
Last Modified:  20 Jul 2018 12:33  
URI:  http://fse.studenttheses.ub.rug.nl/id/eprint/17869 
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