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Dynamically consistent discrete-time Lotka-Volterra competition models

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  • 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.
    Mathematics Subject Classification: Primary: 34-04.


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