Abstract
This study explores the application of generalized complex numbers to derive closed-form analytical solutions for specific classes of nonlinear dynamical systems. Such systems frequently emerge in AI and big data contexts, including optimization processes, neural network training, physical simulations, and real-time predictive modeling. Traditional numerical methods, while broadly applicable, can be computationally intensive and may obscure deeper theoretical insights. We focus on a system of two first-order nonlinear differential equations with homogeneous second-order right-hand sides – a structure that appears in models of data flow, network dynamics, and constrained optimization. By reforming these systems within a unified algebraic framework of generalized complex numbers, we achieve exact solutions, providing a robust benchmark for validating numerical AI algorithms and enhancing computational efficiency in data-driven modeling scenarios.