Dynamically consistent discrete-time Lotka-Volterra competition models

Lih-Ing W. Roeger; Razvan Gelca

doi:10.3934/proc.2009.2009.650

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2009, Volume 2009: 650-658. Doi: 10.3934/proc.2009.2009.650 open access

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Dynamically consistent discrete-time Lotka-Volterra competition models

Lih-Ing W. Roeger^1, and
Razvan Gelca²

1.
Department of Mathematics and Statistics, Box 41042, Texas Tech University, Lubbock, TX 79409-1042
2.
Department of Mathematics and Statistics, Box 41042, Texas Tech University, Lubbock, TX 79409

Received: June 30, 2008

Revised: January 31, 2009

Published: August 2009

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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.

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Mathematics Subject Classification: Primary: 34-04.

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