Quenched Amplification and Tail Shaping in Networked Systems with Memory and Regime Switching

TL;DR

This paper analyzes how memory and regime switching in networked systems can lead to rare extreme events, and proposes a practical intervention strategy to mitigate such tail risks.

Contribution

It introduces a geometric framework for understanding quenched amplification and tail shaping, with a real-time indicator and intervention method for extreme event mitigation.

Findings

Power-law tails in burst-size distributions are linked to regime persistence and memory effects.

A computable online indicator predicts potential extreme amplifications.

A dynamic intervention strategy effectively reduces tail risk without disrupting normal system behavior.

Abstract

Networked systems operating under intermittent adverse conditions and long memory can remain stable on average while exhibiting rare but extreme trajectory-level excursions. We study linear regime-switching network dynamics with Volterra-type memory, formulated through a finite-dimensional lifted ordinary differential equation embedding. Despite finite-horizon annealed boundedness, we show that quenched amplification emerges generically from the interaction of regime persistence, memory accumulation, and non-normal lifted operator geometry. A lower bound on burst-size distributions reveals power-law tails whose exponent is determined by the ratio between unfavorable dwell-time rates and an operator-defined instantaneous growth parameter. This parameter is computable online via the Euclidean logarithmic norm of the lifted operator, yielding a practical early-warning indicator. Building on this structure, we introduce a dynamic data-driven intervention strategy that enforces contraction on demand along rare amplification channels, thereby shaping or truncating tail risk without altering exogenous regime statistics or typical system behavior. The results provide a geometrically grounded and operationally actionable framework for understanding and mitigating extreme events in memory-driven regime-switching systems.