Dynamically consistent discrete-time Lotka-Volterra competition models
Lih-Ing W. Roeger - Department of Mathematics and Statistics, Box 41042, Texas Tech University, Lubbock, TX 79409-1042, 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
Received: July 2008; Revised: February 2009; Published: September 2009.