Stability analysis of periodic solutions to the nonstandard discretized model of the Lotka-Volterra predator-prey system

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.