Agro-ECosystem Studies Based on Lotka-Volterra Modelling and Fourth Order Longe-Kuta Approach

Abstract

In this paper, an agroecosystem food web model based on the Lotka-Volterra equation was constructed to simulate the ecosystem transition from forest to farmland in the state of Mato Grosso, Brazil, covering the producers, consumers at all levels, and soil organic matter dynamics equations. The model was solved using the fourth-order Ronger-Kuta method (RK4), optimised and evaluated by defining an objective function containing economic benefits and ecological sustainability and related assessment indicators, and determining the weights of the indicators using AHP and EWM analysis. On this basis, two new species, leaf-cutting ants and red-eyed wasps, were introduced to adjust the dynamic equations of the model and solved again. The results showed that the introduction of the new species enriched the ecosystem structure, improved the soybean yield and enhanced the ecosystem stability, and the objective function values of the new model were better than the original model, which provided valuable references for ecosystem management and sustainability research.