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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aggarwal A, Klowe M, Moran S, Shor P, Wilber R (1987) Geometric applications of a matrix-searching algorithm. Algorithmica 2:195–208
Alvarez I (2004) Sensitivity analysis of the result in binary decision trees. In: Proceedings of the 15th European conference on machine learning, Lecture notes in artificial intelligence, vol 3201. Springer, Heidelberg, pp 51–62
Alvarez I, Martin S, Mesmoudi S (2010) Describing the result of a classifier to the end-user: geometric-based sensitivity. In: Proceedings of the 22d European conference on artificial intelligence, IOS Press, Amsterdam, pp 835–840
Aubin JP (1991) Viability theory. Birkhauser, Basel.
Bernard C, Martin S (2010) Building strategies to ensure language coexistence in presence of bilingualism. Cemagref. Internal Report.
Carpenter SR, Ludwig D, Brock WA (1999) Management of eutrophication for lakes subject to potentially irreversible change. Ecol Appl 9:751–771
Hirata T (1996) A unified linear-time algorithm for computing distance maps. Inform Process Lett 58(3):129–133
Martin S (2004) The cost of restoration as a way of defining resilience: a viability approach applied to a model of lake eutrophication. Ecology and Society 9(2): 8. http://www.ecologyandsociety.org/vol9/iss2/art8/
Matheron G (1988) Examples of topological properties of skeletons. Image analysis and mathematical morphology, Academic Press, London, pp 217–257
Meijster A, Roerdink J, Hesselink WH (2000) A general algorithm for computing distance transforms in linear time. Morphology and its applications to image and signal processing, pp 331–340
Mesmoudi S, Alvarez I, Martin S, Sicard M, Wuillemin P-H (2009) Geometric analysis of a capture basin: application to cheese ripening process. In: European conference on complex system, October 21–25, 2009, Warwick, UK.
Minett J, Wang W (2008) Modelling endangered languages: the effects of bilinguism and social structure. Lingua 118:19–45
Saint-Pierre P (1994) Approximation of the viability kernel. Appl Math Optim 29:187–209
Saltelli A, Chan K, Scott M (2000) Sensitivity Analysis. Wiley, San Francisco
Serra J (1988) Image Analysis and Mathematical Morphology. Academic Press, London
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Alvarez, I., Martin, S. (2011). Geometric Robustness of Viability Kernels and Resilience Basins. In: Deffuant, G., Gilbert, N. (eds) Viability and Resilience of Complex Systems. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20423-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-20423-4_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20422-7
Online ISBN: 978-3-642-20423-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)