American Institute of Mathematical Sciences

Advanced
2009, 2009(Special): 650-658. doi: 10.3934/proc.2009.2009.650

Dynamically consistent discrete-time Lotka-Volterra competition models

Lih-Ing W. Roeger 1, and  Razvan Gelca 2,

1. 

Department of Mathematics and Statistics, Box 41042, Texas Tech University, Lubbock, TX 79409-1042, United States
2. 

Department of Mathematics and Statistics, Box 41042, Texas Tech University, Lubbock, TX 79409, United States

Received  July 2008 Revised  February 2009 Published  September 2009

Sufficient conditions are given such that the discrete time competition models constructed by applying nonstandard finite difference (NSFD) schemes for the Lotka-Volterra competition models are dynamically consistent. The derived discrete models preserve the positivity of solutions, local stability conditions, boundedness, and the monotonicity of the continuous Lotka-Volterra system. In other words, we are able to construct discrete-time competition models that behave just like the continuous-time Lotka-Volterra competition models.
Keywords: dynamical consistency, NSFD, competition, nonstandard finite-difference schemes, discrete models, Lotka-Volterra.
Mathematics Subject Classification: Primary: 34-04.
Citation: Lih-Ing W. Roeger, Razvan Gelca. Dynamically consistent discrete-time Lotka-Volterra competition models. Conference Publications, 2009, 2009 (Special) : 650-658. doi: 10.3934/proc.2009.2009.650
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