AbstractMany natural, technological, and socio-economic systems evolve under conditions whereexternal pressures increase not only in magnitude but in rate. In such environments, stabilitybecomes a fundamentally dynamic property. System behavior is determined not by theabsolute level of stress, but by the relationship between the speed of environmental changeand the system’s ability to adapt.This work introduces the Theory of Critical Sensitivity (Ψ-theory) — a unified frameworkfor describing the stability of accelerating systems through a single dimensionless controlparameter: Ψ=Aρ where ρ characterizes the effective rate of growth of environmental load and ( A ) representsadaptive capacity.The central principle of the theory is that loss of stability under acceleration is governed bydynamic bifurcation delay. The actual transition to instability does not occur at the staticcritical point but is shifted by a finite amount determined by the acceleration of the controlparameter. For systems near a saddle-node–type instability, this delay follows a universalscaling law: Δλ∼α2/3 This shift defines a critical sensitivity layer — a finite region in parameter space where thesystem remains formally stable but becomes increasingly vulnerable to perturbations.Within this layer, small fluctuations accumulate according to an integral instability condition.Observable deviations grow before the actual transition, producing a measurableearly-warning phase. The characteristic time horizon of this phase follows a universalscaling: H∼α−1/3 Operational stability indicators based on normalized deviations (such as Z-score–typeindices) are shown to represent observable projections of the underlying critical parameter Ψ.Threshold crossing corresponds to entry into the critical sensitivity layer, where the localstability margin becomes comparable to the perturbation flux.● increasing frequency of extreme events,● heavy-tailed distributions of deviations,● non-Poissonian, scale-dependent inter-event intervals,● emergence of 1/f -type fluctuations,● approximate invariance of detection probability, determined by the geometricresidence time within the critical layer.These results imply that modern complex systems tend toward a regime of self-organizedcritical sensitivity, driven not by internal tuning but by external acceleration.Ψ-theory provides a scale-independent and domain-agnostic description of stability foraccelerating systems. It unifies dynamic bifurcation theory, early-warning phenomena, andoperational monitoring within a single physical framework. The theory suggests that theprimary driver of systemic risk is not the level of stress itself, but the growing mismatchbetween environmental acceleration and adaptive response.
Roman Lukin (Tue,) studied this question.