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

TL;DR

This paper develops a mathematical model for biological control of invasive species, introducing ecological damping controls that prevent explosive population growth without harmful chemical or natural enemy interventions.

Contribution

It proposes novel ecological damping strategies to control invasive species, avoiding non-target effects and improving understanding of model regularity, Turing instability, and chaos.

Findings

Controls can prevent finite-time blow-up of invasive populations.

Ecological damping eliminates the need for chemical or natural enemy treatments.

The model exhibits spatio-temporal chaos under certain conditions.

Abstract

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 blow-up 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 earlier work. Lastly, we confirm the existence of spatio-temporal chaos.