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Dynamically consistent discrete-time Lotka-Volterra competition models
Lih-Ing W. Roeger Razvan Gelca
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

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