Soil nutrient dynamics play a vital role in maintaining the productivity and long-term sustainability of agricultural ecosystems. Yet, many existing models fall short by overlooking critical biological feedbacks or oversimplifying the complex interactions between inorganic nutrients, organic matter, and plant biomass. These oversights limit their usefulness in guiding effective and sustainable land management practices. In this study, we aim to address this gap by formulating a comprehensive nonlinear mathematical model that captures the key ecological processes driving nutrient cycling in soils.

We develop a three-dimensional system to represent the dynamic interplay among inorganic nitrogen, soil organic matter, and plant biomass. The model incorporates essential processes such as mineralization, fertilization, nutrient uptake by plants, plant growth, and organic turnover. We establish the positivity and boundedness of model solutions to ensure that they remain biologically meaningful. Equilibrium points, including a plant-free state and a biologically feasible positive state, are identified and analyzed for stability using the Jacobian matrix.

To understand the influence of different factors on system behavior, a detailed sensitivity analysis is performed. This reveals which parameters—such as fertilization rate or mineralization efficiency—most significantly affect long-term nutrient levels and plant biomass. Numerical simulations validate the analytical results and provide great perspective into how the system evolves over time. These simulations illustrate the conditions under which the soil–plant system reaches stability or becomes degraded.

Overall, the proposed model offers a valuable theoretical framework for evaluating soil fertility dynamics and optimizing nutrient management in agricultural settings. It contributes to the understanding of sustainable farming practices and supports data-driven strategies in precision agriculture.