A Functional Framework for Modeling and Predicting Affective Dynamics in Large Language Models

Affect in conversation changes over time, yet limited work has disentangled the influence of current user affect from a model's own recent history. We frame this as a system identification problem over Valence-Arousal-Dominance (VAD) states, learning for each LLM a transition function $E_t^{out}=T_M(E^{in}t,E^{out}t-1)$. We build 24 five-turn scenarios from fixed semantic skeletons, select affectively varied user turns from independently scored candidate banks to realize 18 trajectory families on each VAD dimension, and present identical frozen trajectories to three LLMs from different developers, with a within-family replication across three capability tiers. Transition models are fit on development scenarios and evaluated on held-out scenarios against input-only and previous-response baselines. Across models, current user affect was more predictive than previous response affect alone, but recent response history still added held-out predictive value. The learned dynamics showed consistent same-dimension persistence, nonlinear models improved only modestly over the linear formulation, and a second conversational lag contributed a smaller residual signal. These patterns replicated across GPT-5.6 capability tiers. Together, the results move the study of LLM affect from static response-level measurement toward modeling affect as an interaction-driven dynamical process.