Abstract

Nonlinear dynamical systems arise in numerous scientific and engineering domains, including physics, economics, biology, and control theory. Their complex behavior, sensitivity to initial conditions, and possible chaotic dynamics make accurate modeling and prediction challenging using traditional analytical approaches alone. In recent years, artificial intelligence (AI) techniques have demonstrated strong potential for modeling nonlinear and complex systems through data-driven methods. This paper explores artificial intelligence approaches for modeling nonlinear dynamical systems, focusing on the integration of machine learning techniques with classical mathematical modeling. We consider representative nonlinear systems and analyze how neural networks, regression models, and hybrid AI–mathematical frameworks can be used to approximate system behavior, predict future states, and capture hidden structures in time-series data. Special attention is given to systems exhibiting chaotic behavior, where small perturbations in initial conditions can lead to significant divergence in trajectories. The study presents numerical simulations and comparative analyses between traditional mathematical models and AI-based approaches. The results highlight the advantages of machine learning methods in capturing nonlinear patterns and improving predictive accuracy, especially when analytical solutions are difficult or unavailable. Additionally, we discuss the interpretability of AI models in the context of dynamical systems and outline potential applications in engineering, intelligent control, and data-driven system identification. The proposed framework contributes to the growing intersection between dynamical systems theory and artificial intelligence by demonstrating how AI tools can support the analysis and modeling of complex nonlinear phenomena. This work aims to provide a foundation for future research on hybrid mathematical–AI methods for understanding and predicting complex systems.