Local stability of a discrete competition model derived from a nonstandard numerical method

Abstract

The continuous two-dimensional Lotka-Volterra competition model is converted to a discrete version using a noncanonical symplectic numerical method. The local stability of the differential equations and difference equations are analyzed and compared. We found that the numerical method preserves the local dynamics of the continuous model. The local stability criteria are the same between the continuous model and the discrete model. The discrete-time model is dynamically consistent with its continuous counterpart.