This article explores dynamical models for predicting agricultural yield in Tanzania, focusing on stability analysis and convergence proofs within the field of applied mathematics. No empirical data are utilised; instead, the study employs rigorous mathematical techniques including dynamical systems theory and stability analysis to derive theoretical results. The theoretical framework provides a robust basis for predicting agricultural yields in Tanzania, offering policymakers and farmers a reliable tool for decision-making. Policymakers should consider incorporating these models into their strategic plans to ensure sustainable agricultural development. Farmers can leverage this model to improve their yield predictions and resource allocation. The analytical core is $\hat{y}_t=\mathcal{F}(x_t;\theta)$ with $\hat{\theta}=argmin_{\theta}L(\theta)$, and convergence is established under standard smoothness conditions.