Reading vulnerability in phase portraits: an exercise in probabilistic resilience assessment

Within the quest for quantitative methods to assess critical infrastructure vulnerabilities, a method is proposed to assess system vulnerability in terms of probabilities that the system undergoes significant changes, or even disintegrates under progressive stress – a natural approach in, e.g., the trade of material testing. Whilst, in the context, the "system" is seen as the phase portrait of a critical process animating its structure, the stress test boils down to inducing random fluctuations of incremental amplitude in the model control parameters and observing the ensuing distortions in the process phase portraits. Three classes of distortions are monitored for the purpose of evaluating a system failure relative frequency: innocuous distortions: that preserve phase portrait topology and thereby system stability and, to some extent, its predictability and manoeuvrability; crippling distortions: that change phase portrait topology and thereby a system's stability and would, generally, severely alter predictability and manoeuvrability whilst, however, leaving the system in a bound state; catastrophic distortions: taking the system out of the realm of bound states and thereby having it disintegrated. The method is as general as the ability to define a system in terms of its processes, and the processes in terms of iterated maps, or ODE (ordinary differential equation) flows.