Mathematical Modeling on the Effect of Flood on Farmland: A Nonlinear Dynamical Systems Approach

Objectives This paper provides a three-dimensional nonlinear ordinary differential equation (ODE) model to clearly understand the effects of flooding on agricultural farmlands. The model uses three interacting state variables: farmland productivity F(t), soil quality index S(t), and floodwater level W(t). The novelty of this work lies in: (i) explicit mechanistic coupling between all three variables, including positive feedback from soil quality to productivity and negative feedback from vegetation to floodwater (ii) identification of critical bifurcation thresholds using rigorous stability analysis; and (iii) quantification of synergistic effects from combined management interventions. Material and Methods Existence and uniqueness of solutions were established using the Picard-Lindelöf theorem; all biologically possible equilibrium points were identified, and their stability was assessed through the Routh-Hurwitz criteria. Results Extensive numerical modeling was carried out using MATLAB and sensitivity analysis was applied to identify the most critical parameters governing system behavior: drainage capacity (δ), flood input intensity (μ), and the crop damage coefficient (α). The model reveals critical thresholds i.e at drainage capacity 0.30 and flood input 0.70, above which the system reaches the irreversible degradation regimes. In combinations, there are synergistic advantages, with up to 32.8% productivity gain recorded when drainage infrastructure, flood-resistant crops, and soil conservation have been integrated into management. Conclusion The results show that thresholds for drainage and flood-input parameters exist that govern the extent of degradation of farmland productivity during flooding, and that integrated management strategies are considerably more effective than single interventions, providing actionable evidence-based targets in agricultural resilience planning in flood-prone areas.