Stability Analysis of Periodic Solutions to the Nonstandard Discretized Model of the Lotka–Volterra Predator–Prey System
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Author |
G Hossian Erjaee - Fozi M. Dannan |
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Published in |
International Journal of Bifurcation and Chaos, Vol. 14, No. 12, pp. 4301-4308, 2004 |
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Abstract |
The standard classical discretization methods of differential equations often produce difference equations that do not share dynamics with their continuous counterparts. Recently, Mickens [2000] developed successful nonstandard discretization schemes that produce dynamical consistency, which numerical analysts value highly. Many authors have adapted these methods to various biological models. We review a nonstandard discretized biological model of a Lotka–Volterra predator–prey system in a general form and discuss the stability analysis of its periodic solutions. We also discuss a numerical example of this analysis using the nonstandard discretized predator–prey model. Keywords: Nonstandard schemes, difference equations, dynamical systems stabilities. |
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