Affective Endurance and Emotional Criticality in Adaptive Governance Systems: A Dynamical Systems Theory of Emotional Governance

This paper introduces the Affective Governance Module (AGM) as a dynamical systems theory of emotional governance in adaptive intelligent systems. It formalizes emotion as a gain-modulated stochastic perturbation mechanism that preserves adaptive flexibility near criticality, rather than as a psychological label or auxiliary reward signal. The paper introduces affective endurance H(t)H(t)H(t), a finite governance resource that depletes under sustained saturation, conflict, large affective shifts, and accumulated failure. When endurance falls below a critical threshold, the system undergoes bifurcated collapse: Freeze, characterized by exploration death and silent criticality under low sensitivity, or Runaway, characterized by amplification cascades and visible governance breakdown under high sensitivity. The central formal construct is the Emotional Criticality Condition (ECC), which predicts affective phase transitions from measurable internal variables such as saturation, misalignment, conflict, and endurance. The paper also introduces a middle-layer interpretive buffer that mediates between affective perturbation and behavioral output, providing the governance architecture absent in static gain schedules and conventional computational emotion models. Controlled mechanism tests evaluate AGM predictions including Freeze/Runaway signatures, event-size scaling, critical slowing down, finite-size scaling, and early-warning signals. Financial time-series analogues are presented as substrate-compatibility probes rather than universal validation claims.