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In this work we develop and analyze a mathematical model of biologicalcontrol to prevent or attenuate the explosive increase of an invasive speciespopulation in a three-species food chain. We allow for finite time blow-up inthe model as a mathematical construct to mimic the explosive increase inpopulation, enabling the species to reach "disastrous" levels, in a finitetime. We next propose various controls to drive down the invasive populationgrowth and, in certain cases, eliminate blow-up. The controls avoid chemicaltreatments and/or natural enemy introduction, thus eliminating variousnon-target effects associated with such classical methods. We refer to thesenew controls as "ecological damping", as their inclusion dampens the invasivespecies population growth. Further, we improve prior results on the regularityand Turing instability of the three-species model that were derived in earlierwork. Lastly, we confirm the existence of spatio-temporal chaos.

Biological control via "ecological" damping: An approach that attenuates non-target effects