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Geometric robustness of viability kernels and resilience basins

Isabelle Alvarez 1, 2 Sophie Martin 2 
Abstract : The definition of resilience described in Chap. 2 applies to dynamical systems whose dynamics are modelled by controlled differential equations and in which some properties of interest are defined by a subset of the state space (the constraint set). These dynamical systems, when they model environmental or socioeconomic systems, are subject to uncertainties. Moreover, the properties of interest are rarely known with absolute certainty and accuracy. Viability theory can take into account only a part of these uncertainties, considering a set of velocity vectors rather than a single vector. Therefore, performing sensitivity analysis (like in Saltelli et al. 2000) appears as a good solution to assess the impact of the other parameters of the dynamics, and also the impact of slight modifications of the boundary of the constraint set on the viability kernel and its capture basin.
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Isabelle Alvarez, Sophie Martin. Geometric robustness of viability kernels and resilience basins. Viability and resilience of complex systems: concepts, methods and case studies from ecology and society., Springer, pp.193-218, 2011, 978-3642204227. ⟨10.1007/978-3-642-20423-4_8⟩. ⟨hal-01286979⟩



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