Resilience and vulnerability have been growingly used among diverse scientific communities in order to describe the impacts of stresses and hazards on social and / or environmental systems. Yet, it often remains unclear what is precisely meant by these two concepts when they are used. This is why a formal definition is proposed for both of them, using stochastic controlled dynamical systems as well as the concepts and tools of a control theory called viability. The mathematical formulation provides an unequivocal reference, while being flexible enough to allow for the design of varied resilience and vulnerability indicators.
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