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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
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Abstract |
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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. |
Keywords
mathematical model, competition, bifurcation
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Mathematical Subject Classification 2010
Primary: 97M60
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Milestones
Received: 31 August 2011
Revised: 15 March 2012
Accepted: 22 May 2012
Published: 14 June 2013
Communicated by Suzanne Lenhart
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Authors |
| John Alford | |
| Mathematics and Statistics Sam Houston State University P.O. Box 2206 Hunstville, TX 77341-2206 United States |
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| Curtis Balusek | |
| Mathematics and Statistics Sam Houston State University P. O. Box 2206 Huntsville, TX 77341-2206 United States |
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| Kristen M. Bowers | |
| Department of Chemistry Sam Houston State University P. O. Box 2117 Huntsville, TX 77341-2117 United States |
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| Casey Hartnett | |
| Mathematics and Statistics Sam Houston State University P.O. Box 2206 Huntsville, TX 77341-2206 United States |
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