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Dynamically consistent discrete-time Lotka-Volterra competition models

Pages: 650 - 658, Issue Special, September 2009

 Abstract        Full Text (144.8K)              

Lih-Ing W. Roeger - Department of Mathematics and Statistics, Box 41042, Texas Tech University, Lubbock, TX 79409-1042, United States (email)
Razvan Gelca - Department of Mathematics and Statistics, Box 41042, Texas Tech University, Lubbock, TX 79409, United States (email)

Abstract: 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:  discrete models, dynamical consistency, competition, Lotka-Volterra, nonstandard finite-difference schemes, NSFD
Mathematics Subject Classification:  Primary: 34-04

Received: July 2008;      Revised: February 2009;      Published: September 2009.