Large Language Models as Tools for Symbolic Discovery and Analysis of Nonlinear Dynamical Systems

This paper investigates the potential role of Large Language Models (LLMs) as symbolic-assistance tools for theoretical analysis and exploratory discovery in nonlinear dynamical systems. As a case study, a three-dimensional chaotic system exhibiting a remarkable parameter-exchange property is examined within a structured human–LLM interaction framework. Guided by a sequence of four predefined research questions, the advanced LLM ChatGPT-5 Academic Assistant Pro identified that the observed parameter-exchange phenomenon is associated with an underlying scaling symmetry of the system. Based on the generated symbolic reasoning, the model further provided a mathematical interpretation of the phenomenon and formulated a generalized scaling lemma describing conditions under which similar parameter-exchange symmetries may arise in three-dimensional dynamical systems. In addition, the LLM suggested relevant classes of nonlinear systems satisfying the same structural constraints, as well as other possible symmetry types potentially associated with the studied system. This study treats the LLM as a probabilistic symbolic hypothesis-generation assistant capable of supporting exploratory reasoning in nonlinear dynamics and chaos theory. Overall, the findings highlight the potential of human–LLM collaborative frameworks for symbolic exploration and mathematical interpretation of complex dynamical systems.