Estimation the parameters of Lotka–Volterra model based on grey direct modelling method and its application

In this paper, based on the grey direct modelling method, we present linear programming method to estimate the parameters of the Lotka–Volterra model under the criterion of the minimization of mean absolute percentage error (MAPE) (some authors called average relative error). Then use Lotka–Volterra model to analysis the relationship between two variables, and use discrete Lotka–Volterra model to forecast the two variables respectively, two practical examples are chosen for practical tests of this method, the results show that this method can provide empirical support for long-term qualitative analysis and obtain short-term quantitative prediction results, these have shown that this method is effective and applicable.