Vol. 5, No. 4, 2012

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A mathematical model of biocontrol of invasive aquatic weeds

John Alford, Curtis Balusek, Kristen M. Bowers and Casey Hartnett

Vol. 5 (2012), No. 4, 431–447

In this paper we modify the classical Lotka–Volterra differential equations to analyze competition between two aquatic plant species, a submersed plant and a free-floating plant. We formulate and analyze a system of three differential equations that control the dynamics of the free-floating plant biomass and both aboveground and belowground biomass for the submersed plant. We investigate our model to understand how plant competition is affected by grass carp herbivory on the submersed plant’s aboveground biomass. We analyze both a reduced model, for which the submersed plant is assumed to have constant belowground biomass, and the full model. In each case, we compute stability of equilibria and derive a minimal grass carp stocking rate such that the free-floating plant may dominate the submersed plant. For the reduced model we show that the rate at which grass carp are stocked may exhibit a hysteresis effect.

mathematical model, competition, bifurcation
Mathematical Subject Classification 2010
Primary: 97M60
Received: 31 August 2011
Revised: 15 March 2012
Accepted: 22 May 2012
Published: 14 June 2013

Communicated by Suzanne Lenhart
John Alford
Mathematics and Statistics
Sam Houston State University
P.O. Box 2206
Hunstville, TX 77341-2206
United States
Curtis Balusek
Mathematics and Statistics
Sam Houston State University
P. O. Box 2206
Huntsville, TX 77341-2206
United States
Kristen M. Bowers
Department of Chemistry
Sam Houston State University
P. O. Box 2117
Huntsville, TX 77341-2117
United States
Casey Hartnett
Mathematics and Statistics
Sam Houston State University
P.O. Box 2206
Huntsville, TX 77341-2206
United States