Network resilience optimisation of complex systems

This paper presents a method for the design for resilience of complex systems under uncertainty. In this approach, the complexity of the system is captured by a network formulation. Each node i is completely determined by two indicators: a performance fi and a functionality ci. Both these measures depend on time, decision and uncertain variables. In particular, we suggest the functional measure of resilience. The node resilience depends on the evolution over time of its state xi which is solution of a differential equation. Bifurcation theory is used to continuously model transitions between fully functioning and degraded states, disruptions and shocks that could affect the node. This work shows how to exploit the network properties and to optimise the global connected resilience emerging from the coupled dynamics of the single nodes.