Developing and Analysing High-Order Ordinary Differential Equations to Predict Agricultural Asset Growth and Loss Under Varying Environmental Stressors
Keywords:
Agricultural Modeling, Environmental Stressors, Crop Yield Prediction, Nonlinear Dynamics, Numerical SimulationAbstract
This work develops a higher-order nonlinear ODE model for analysing the growth and decline of agricultural assets under diverse environmental pressures. Environmental parameters such as temperature, rainfall, fertilisation, and insect damage are modelled as time-dependent forcing functions that characterise the dynamics of the agricultural production system. The model is solved numerically using the fourth-order Runge-Kutta method, implemented in a Python programming environment, and calibrated with actual agricultural production data collected from 2010 to 2022. As shown in the results, the model accurately captures the long-term growth of agricultural produce. The model performs well, with an MAE of 13.99 kg/ha and an RMSE of 15.42 kg/ha. From the graph, it is clear that the model accurately reproduces both the macro- and micro-dynamics of agricultural produce. Furthermore, the system exhibits stable growth and convergent dynamics towards equilibrium, as shown in its phase dynamics. However, underestimation may occur during periods of rapid growth in crop yields, with residual structures indicating the influence of external variables not included in the model. Despite these problems, the results show that higher-order ODEs can be effectively used to inform decision-making in agriculture.
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