Vol. 5, No. 4, 2012

Download this article
Download this article For screen
For printing
Recent Issues
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 3
Volume 6, Issue 2
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 5
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
Cover Page
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Author Index
Coming Soon
Contacts
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
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
Abstract

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
Mathematical Subject Classification 2010
Primary: 97M60
Milestones
Received: 31 August 2011
Revised: 15 March 2012
Accepted: 22 May 2012
Published: 14 June 2013

Communicated by Suzanne Lenhart
Authors
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