In this work we develop and analyze a mathematical model of biological control to prevent or attenuate the explosive increase of an invasive species population in a three-species food chain. We allow for finite time blowup in the model as a mathematical construct to mimic the explosive increase in population, enabling the species to reach “disastrous” levels, in a finite time. We next propose various controls to drive down the invasive population growth and, in certain cases, eliminate blow-up. The controls avoid chemical treatments and/or natural enemy introduction, thus eliminating various non-target effects associated with such classical methods. We refer to these new controls as “ecological damping”, as their inclusion dampens the invasive species population growth. Further, we improve prior results on the regularity and Turing instability of the three-species model that were derived in . Lastly, we confirm the existence of spatio-temporal chaos.
Parshad, Rana D.; Black, Kelly; Quansah, Emmanuel; and Beauregard, Matthew, "Biological control via "ecological" damping: An approach that attenuates non-target effects" (2015). Faculty Publications. 14.
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