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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Extinction in discrete, competitive, multi-species patch models

Pages: 1583 - 1590, Volume 20, Issue 6, August 2015      doi:10.3934/dcdsb.2015.20.1583

 
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David M. Chan - Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284, United States (email)
Matt McCombs - Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284, United States (email)
Sarah Boegner - Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284, United States (email)
Hye Jin Ban - Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284, United States (email)
Suzanne L. Robertson - Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284, United States (email)

Abstract: In this paper we extend the results of Franke and Yakubu in [5] for extinction in discrete competitive patch models. For a system of $n$ species on $m$ patches, we define conditions under which one species is a ``superior competitor" to another and show that this is sufficient for one species to drive another to extinction. We also illustrate the result with an example for three species on three patches.

Keywords:  Competition, extinction, patch models, Lyapunov function, difference equations.
Mathematics Subject Classification:  Primary: 92B05, 39A30; Secondary: 39A60.

Received: November 2013;      Revised: December 2014;      Available Online: June 2015.

 References