Abstract Accelerating complex adaptive systems — including digital information ecosystems, human cognition, plasma confinement, and financial networks — exhibit rate-induced instabilities that conventional quasi-static thresholds fail to anticipate. Optimal System Dynamics (OSD v1. 2) introduces a formal field-theoretic framework centered on the dimensionless critical sensitivity field Ψ (x, t), governed by the reaction-diffusion equation with a rate-induced term k α^2/3. Cognitive debt is interpreted as accumulated instability energy exceeding adaptive capacity. The framework explicitly incorporates an endogenous natural recovery mechanism — represented by the relaxation term −γ Ψ — as a mathematically necessary component that enables dynamic equilibrium and debt repayment through rest, consolidation, and offline periods.
Р С Лукин (Sat,) studied this question.