title: Biological control via "ecological" damping: An approach that attenuates non-target effects.
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, that functions as a top predator, 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", and uncontrollable population levels, in a finite time. We next improve the mathematical model and incorporate controls that are shown to drive down the invasive population growth and, in certain cases, eliminate blow-up. Hence, the population does not reach an uncontrollable level. 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 Parshad et al. (2014). Lastly, we confirm the existence of spatiotemporal chaos.
authors.affiliation: Department of Mathematics, Clarkson University, Potsdam, NY 13699, USA. Electronic address: rparshad@clarkson.edu.
authors.forename: Rana D
authors.initials: RD
authors.lastname: Parshad
authors.affiliation: Department of Mathematics, Clarkson University, Potsdam, NY 13699, USA. Electronic address: quansaek@clarkson.edu.
authors.forename: Emmanuel
authors.initials: E
authors.lastname: Quansah
authors.affiliation: Department of Mathematics, Clarkson University, Potsdam, NY 13699, USA. Electronic address: kblack@clarkson.edu.
authors.forename: Kelly
authors.initials: K
authors.lastname: Black
authors.affiliation: Department of Mathematics & Statistics, Stephen F. Austin State University Nacogdoches, TX 75962, USA. Electronic address: beauregama@sfasu.edu.
authors.forename: Matthew
authors.initials: M
authors.lastname: Beauregard
mesh_terms: D000818:Animals; D003198:Computer Simulation; D017753:Ecosystem; D020387:Food Chain; D058865:Introduced Species; D055641:Mathematical Concepts; D008954:Models, Biological; D017711:Nonlinear Dynamics; D011157:Population Dynamics / Q000706:statistics & numerical data; D011235:Predatory Behavior
keywords: Finite time blow-up; Global existence; Spectral methods; Three-species food chain