Modeling the impact of detritus-based irrigation on agricultural crop production - Misra, Arvind Kumar; Shukla, Prinsi (Nonlinear Analysis: Modelling and Control, 2026)
The excessive use of chemical fertilizers in agricultural farms poses a serious threat to nearby water bodies, such as lakes, ponds, etc., by causing algal blooms in these water bodies and also put agricultural sustainability at risk. This study deals with the use of algae-rich pond water for irrigation, which impacts soil fertility through organic detritus. A nonlinear mathematical model is formulated to analyze the ecological and agronomic impacts of this irrigation approach. The formulation of the model takes into account that the detritus-based pond water used for irrigation initially benefits the crop growth; but once it exceeds a certain threshold, reduces the crop yield. Furthermore, the model demonstrates how nature-based solutions can be strategically integrated into agricultural system to achieve long-term resilience. The study identifies key thresholds and behavioral transitions by detecting a saddle-node, transcritical, and Hopf bifurcations within the proposed mathematical model. To support analytical findings, we conduct numerical simulations that provide a strong evidence of the agricultural ecosystem’s resilience particularly in maintaining the crop yield under the modeled irrigation conditions. These simulations underscore the potential for managing detritus density to optimize crop productivity while minimizing ecological risks. Findings of this study can support the environment-friendly irrigation policies suited to different agroecological regions. Study reveals that detritus-based irrigation promotes crop productivity up to a critical threshold of detritus input, beyond which its effects turn inhibitory. Simultaneously, it suppresses algal blooms, thereby uncovering a natural self-regulating mechanism with significant implications for sustainable irrigation practices and nutrient management policies.
Keywords: mathematical model; agriculture; algae; detritus; bifurcations