Mathematical Modeling and Analysis on Nitrogen Fixation for Controlling Sunflower Oil Production

Abstract

Nitrogen fixation plays a vital role in enhancing crop yields, yet its inefficient utilization remains a critical challenge in sustainable agriculture. In sunflower oil production, imbalances in nitrogen availability can lead to reduced growth and oil quality, necessitating effective management strategies. To address these challenges, we have developed a newly proposed mathematical model using a system of ordinary differential equations that has been studied both analytically and numerically. Positivity and boundedness of the model's solution, stability at the equilibrium points, and characteristics with respect to state variables have been studied as some parts of the analytical solution. Also, the numerical solution has been done using the Runge–Kutta 4th order technique. The findings of this study reveal that both excessive and insufficient nitrogen application can negatively impact the expected oil production from sunflower crops as well as maintaining soil pH within the standard range, which is essential for rising oil yield. Furthermore, the results indicate that applying nitrogen fertilizer at half the recommended rate between $30^{th}$ and $40^{th}$ days, followed by the full rate between the $40^{th}$ and $50^{th}$ days, results in the same expected oil production as applying the full recommended amount evenly throughout the period $30^{th}$ to $50^{th}$ days. Therefore, this study emphasizes the need for precise nitrogen management methods to improve oil production.