A simple sufficient condition for stability and robust stability of a discrete Lotka-Volterra model

Abstract

In a recent paper by Q. Din, a discrete Lotka-Volterra model was considered and the local asymptotic stability of equilibrium points has been discussed. The unique positive equilibrium point is proved to be stable under a very complicated sufficient condition, which involves all six positive parameters from the model. Using a different approach, we will come to the same conclusion under one very simple condition, involving only four parameters. For all numerical examples considered in the above mentioned paper, our new condition is satisfied. Moreover, our new approach allowed us to discuss robust stability, which is extremely important in reality, since it covers possible empirical noise in the input data of the model.