STABILITY ANALYSIS OF PERIODIC SOLUTIONS TO THE NON-STANDARD DISCRETIZATION MODEL OF THE LOTKA-VOLTERRA PREDATOR-PREY SYSTEM

Abstract

The standard classical discretization methods of differential equations often produce difference equations that do not share dynamics with their continuous counterparts; Recently,[4] has developed successful non-standard discretization schemes that produce dynamical consistency, which numerical analysis value highly. Many authors have adapted these methods to various biological models. We reviewed a non-standard discretized biological model of a Lotka-Volterrs Predator-Prey system in a general form and discussed the stability analysis of its periodic solutions. We also discussed a numerical example of this analysis using the non-standard discretized Predator-Prey model the name of executed program for drawing and calculation is “MATLAB 7.0”.