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arXiv · 2604.08112

Resilience as a Dynamical Property of Risk Trajectories in CPSoS

Elisabeth Vogel·Peter Langendörfer
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Abstract

Resilience in cyber-physical systems of systems (CPSoS) is often assessed using static indices or point-in-time metrics that do not adequately account for the temporal evolution of risk following a disruption. This paper formalizes resilience as a functional of the risk trajectory by modelling risk as a dynamic state variable. It is analytically shown that key resilience properties are structurally determined by maximum deviation (peak) and effective damping, and that cumulative risk exposure depends on their ratio. A simplified energy-dependent system illustrates the resulting differences in peak magnitude, recovery dynamics, and cumulative impact. The proposed approach links resilience assessment to stability properties of dynamic systems and provides a system-theoretically consistent foundation for the analysis of time-dependent resilience in CPSoS.

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Elisabeth Vogel, Peter Langendörfer. 2026-04-09. Resilience as a Dynamical Property of Risk Trajectories in CPSoS. https://arxiv.org/abs/2604.08112

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