Learning System Stability Model: A Minimal Dynamical Framework for Adaptive Learning Systems

This paper introduces the Learning System Stability Model (LSSM), a minimal dynamical framework describing the stability conditions of adaptive learning systems. The model proposes a structural stability law stating that learning remains stable only when the learning load does not exceed the system’s integration capacity: L ≤ Icap (E, S, P) where integration capacity depends on processing structure (P), available energy or resources (E), and the system’s stability state (S). Within this framework, adaptive learning emerges as a cyclic process: E → S → C → L → I → S' where energy supports stability, stability enables exploration, exploration drives learning, and integration produces a new stable state. The model provides a unified stability principle applicable to biological cognition, human psychological development, and artificial learning systems. The framework also suggests architectural implications for adaptive AI systems in which learning must be actively regulated to prevent instability.