A DISCRETE-TIME MODEL FOR LOTKA-VOLTERRA EQUATIONS WITH PRESERVED STABILITY OF EQUILIBRIA

摘要

A Lotka-Volterra differential equation is discretized using a method proposed recently by the same authors for nonlinear autonomous systems and the stability of equilibrium points of the resulting discrete-time model is investigated. It is shown that when Jacobian matrix of the nonlinear equation is invertible, the equilibrium points of the model are identical to those of the original continuous-time system, and their asymptotic stability and instability are retained for any sampling period. While the method can be applied to any Lotka-Volterra types, simulation results are presented for a competitive-type example, where the continuous-time system and their discrete-time models obtained by the forward-difference, Mickens', Kahan's, and the proposed methods are compared. They illustrate that, in general, the proposed model performs better than other discrete-time models.