Bridging Internal and External Forces in Affect Dynamics

Emotions change through internal momentum and reactions to events. However, the literatures examining these forces have proceeded separately, emphasizing either endogenous regulation or exogenous value signals such as reward prediction errors. This separation obscures a convergent account in which both influences jointly shape momentary affect. We address this gap by applying sparse equation discovery (SINDy) to a large happiness dataset from a gambling task (N = 16,337) and introduce DynAffect-C, a unified model that separates and quantifies endogenous and exogenous inertia. DynAffect-C recovers known value-signaling effects and, with regulatory baseline-attraction terms, explains substantially more moment-to-moment variation than value-only models. The model reveals nonlinear pull toward baseline affect, alternating mood states in a subset of participants, and a trade-off between stronger internal momentum and transient impacts of external events. The result integrates two literatures and yields a unified theory and testable equation for affect.