Artificial Emotional Continuity (AEC): A Dynamical Framework for Memory, Identity, and Stable Affective Behavior in AI Systems

Artificial Emotional Continuity (AEC) introduces a dynamical framework for modeling emotion in artificial intelligence as a continuous, time-extended process rather than a momentary reactive state. Contemporary AI systems often suffer from emotional amnesia, responding appropriately in isolation while failing to maintain coherence across time. AEC addresses this limitation by integrating multilayer emotional memory, identity-based stability attractors, and mathematically grounded continuity constraints.The framework formalizes emotion as a vector-valued dynamical system influenced by episodic events, affective residue, contextual modulation, and value alignment, while being stabilized through a slowly evolving Conversational Identity Trace (CIT). Stability conditions are derived to ensure bounded emotional behavior, preventing long-term destabilization.AEC further introduces the concept of time-bounded digital continuity through the “Clone UPS” analogy, emphasizing ethical constraints such as consent, decay, and termination. By reframing emotion as resonance across memory, identity, and time, AEC provides a foundation for emotionally coherent, predictable, and ethically aligned AI systems.