Publications of LISC related to Viability Theory

Viability of specific systems or connecting viability and other domains

  • S. Martin, I. Alvarez, J.D. Kant, Micro/macro viability analysis of individual-based models: Investigation into the viability of a stylized agricultural cooperative, 2014
  • C. Rougé, J.D. Mathias, G. Deffuant, Relevance of control theory to design and maintenance problems in time-variant reliability: The case of stochastic viability, 2014
  • W. Wei, S. Martin, I. Alvarez, Sustainability analysis: Viability concepts to consider transient and asymptotical dynamics in socio-ecological tourism-based systems, 2013
  • C. Bernard, S. Martin, Comparing the sustainability of different action policy possibilities: Application to the issue of both household survival and forest preservation in the corridor of Fianarantsoa, 2013
  • N. Sicard, N. Perrot, R. Reuillon, S. Mesmoudi, I. Alvarez, S. Martin, A viability approach to control food processes: Application to a Camembert cheese ripening process, 2012
  • C. Bernard, S. Martin, Building strategies to ensure langage coexistence in presence of bilingualism, 2012
  • L. Chapel, G. Deffuant, S. Martin, C. Mullon, Defining yield policies in a viability approach, 2008

Defining resilience within Viability Theory

The original idea of defining resilience within the framework of viability theory comes from Martin (2004). Since then, many works of LISC researchers have further developed this area of research.

  • C. Rougé, J.D. Mathias, G. Deffuant
    Extending the viability theory framework of resilience to uncertain dynamics, and application to lake eutrophication
    Ecological Indicators 29, 2013
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  • S. Martin, G. Deffuant, J.M. Calabrese
    Defining resilience mathematically: from attractors to viability
    Viability and resilience of complex systems: ; concepts, methods and case studies from ecology and society (p. 15-36), Springer, 2011
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  • G. Deffuant, N. Gilbert
    Viability and resilience of complex systems: concepts, methods and case studies from ecology and society
    Springer, 2011
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  • L. Chapel, X. Castello, C. Bernard, G. Deffuant, V. Eguiluz, S. Martin, M. San Miguel
    Viability and resilience of languages in competition
    PLoS One 5 (1 (e8681)), 2010
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  • S. Martin
    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), 2004
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Defining robustness within viability Theory

  • S. Mesmoudi, I. Alvarez, S. Martin, R. Reuillon, M. Sicard, N. Perrot
    Coupling geometric analysis and viability theory for system exploration: Application to a living food system
    Journal of Process Control 24 (12), 2014
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  • I. Alvarez, S. Martin
    Geometric robustness of viability kernels and resilience basins
    Viability and resilience of complex systems: concepts, methods and case studies from ecology and society (p. 193-218), Springer, 2011
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Defining vulnerability

  • J.B. Rouquier, I. Alvarez, R. Reuillon, P.H. Wuillemin
    A kd-tree algorithm to discover the boundary of a black box hypervolume
    Annals of Mathematics and Artificial Intelligence 75 (3), 2015
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  • C. Rougé, J.D. Mathias, G. Deffuant
    Vulnerability: from the conceptual to the operational using a dynamical system perspective
    Environmental Modelling & Software 73, 2015
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Computational issues

  • A. Brias, J.D. Mathias, G. Deffuant
    Accelerating viability kernel computation with CUDA architecture: application to bycatch fishery management
    Computational Management Science 13 (3), 2016
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  • G. Deffuant, L. Chapel, S. Martin
    Approximating viability kernels with support vector machines
    IEEE Transactions on Automatic Control 52 (5), 2007
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  • O. Bokanowski, S. Martin, R. Munos, H. Zidani
    An anti-diffusive scheme for viability problems
    Applied Numerical Mathematics 56 (9), 2006
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