Competitive Instability in Judo: The Hidden Mechanism within an AI-Driven Non-Linear Dynamics Framework

Abstract: This study presents a unified nonlinear dynamical framework for understanding, modelling, and teaching competitive judo. The Tori Uke dyad is formalised as a constrained multi body system whose behaviour emerges from symmetry breaking,coupling dynamics and transitions between attractor basins.Two fundamental instability archetypes rotational collapse Uchi mata type and gravitational lever collapse Seoi otoshi,suwari version, are identified as the core pathways through which all throwing techniques evolve.A Functional Instability Index is introduced as a dimensionless order parameter integrating geometric, dynamic, and coupling related variables, enabling the quantification of critical transitions such as Kuzushi,Tsukuri and Kake.Fractional Brownian Motion models the global displacement of the dyad, linking tactical exploration to the persistence structure of the interaction. An AI based pipeline extracts instability signatures from high frequency competition video, providing objective measures such as finite-time Lyapunov exponents,attractor topology and coupling stiffness.Building on these principles, a three level teaching framework is proposed, shifting judo pedagogy from a technique centred to an instability centred approach.This study establishes the first theoretical foundations for a predictive science of judo performance and outlines future directions for empirical validation, athlete monitoring, injury risk modelling and cross sport applications. .