Defining resilience and vulnerability within the framework of viability theory and stochastic controlled dynamical systems

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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