This study innovatively introduces the nonlinear dynamics framework into the field of graduate mental health research, focusing on the unexplored correlation between graduate students’ submissive reply behaviors (e.g., "Okay, professor", "Received", "Understood") in academic communication with supervisors and academic anxiety. A 12-month longitudinal cohort study was conducted among 317 postgraduate students from comprehensive universities, science and engineering universities, and medical universities in eastern, central, and western China. We quantified five core indicators of submissive replies: reply frequency, lexical category, response latency, periodic fluctuation, and emotional valence of wording, combined with the Generalized Anxiety Disorder-7 (GAD-7) scale, Academic Anxiety Scale for Graduate Students (AAGS), and nonlinear dynamic modeling methods (including phase space reconstruction, Lyapunov exponent calculation, and bifurcation analysis). Results demonstrated that: (1) Submissive reply features and graduate anxiety present a significant nonlinear dynamic relationship rather than a simple linear correlation, with obvious chaotic characteristics and periodic bifurcation phenomena; (2) High-frequency, single-type, and rigid submissive replies (e.g., repetitive "Received" without emotional information) are strong predictive signals of moderate-to-severe academic anxiety (AUC = 0.876, sensitivity = 82.3%, specificity = 81.5%); (3) Nonlinear dynamic models based on reply behavioral indicators achieve high-precision prediction of anxiety changes (R² = 0.892), outperforming traditional linear regression models by 37.4%; (4) The periodic mutation of reply behaviors can serve as an early warning marker for anxiety deterioration 4–6 weeks in advance. This study breaks through the limitations of traditional mental health research relying on self-report scales, pioneers the computational quantification of micro-interactive behaviors in supervisor-student relationships, and provides an objective, non-invasive, real-time prediction method for identifying high-anxiety graduate students. The findings have important theoretical value for nonlinear psychological dynamics and practical significance for the early intervention of graduate mental health crises.