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Resilience and vulnerability from a stochastic controlled dynamical system perspective

Resilience and vulnerability from a stochastic controlled dynamical system perspective. Charles Rougé, Jean-Denis Mathias and Guillaume Deffuant. The viability framework for resilience. Example : The case of lake eutrophication. (Carpenter et al., 1999). Phosphorus input L.

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Resilience and vulnerability from a stochastic controlled dynamical system perspective

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  1. Resilience and vulnerability from a stochastic controlled dynamical system perspective Charles Rougé, Jean-Denis Mathias and Guillaume Deffuant

  2. The viabilityframework for resilience

  3. Example: The case of lake eutrophication (Carpenter et al., 1999) Phosphorus input L Bounded!!! (by U>0) Lake (Phosphorus concentration P) Outflow Inflow Algae

  4. Deterministicviability: single trajectories Event Events

  5. Part I Resilience of a stochastic controlled dynamical system

  6. Impact of uncertainty on the viabilitykernel

  7. Multiplicity of recoverytrajectories Events

  8. Resilience in a stochasticdynamical system Recoveryisdefined by getting back to the stochasticviabilitykernel Centrality of the probability of recoveryafter a given date: the Probability of resilience No longer a unique measure of recovery but possibility to derivestatistics.

  9. Resiliencestatistic:expectedrecovery date

  10. Resiliencestatistic: maximal recovery time (99% confidence)

  11. Resiliencestatistic: probability of resilience

  12. Part II Vulnerability as a measure of future harm

  13. Harm: a value judgement on a state Threshold of harm Properties Ecologicalharm Quadraticincreasewith P Economicharm Increaseslinearly as L decreases

  14. Definingvulnerability One associatesharm values to a trajectory: • Sum of staticharm values (costcriterion) • Crossing of a threshold (viabilitycriterion) Vulnerabilityis a statistic on the distribution of harm values: • Expected value of the cost • Exit probability (crossing of a threshold) • Value-at-risk (e.g. worst 1%) of the cost Interest in low-vulnerabilitykernels.

  15. Vulnerability as total cost Τ=100

  16. Vulnerability as exit probability Stochasticviabilitykernel!!!

  17. Part III Towards a resilience-vulnerability framework

  18. Conceptualdefinitions Resilience:capacity to keep or recoverpropertiesafter a hazard, disturbance or change. • Probability of recoveryat date t • Statistic on a recovery time distribution Vulnerability: a measure of future harm(Hinkel, 2011). • Statistic on an exit probability • Statistic on a cost distribution

  19. Combiningresilience and vulnerability Resilience: capacity to recover Vulnerability: harmexperienced (equivalent to a restorationcost) ? Dynamicsafetycriterion (or property of interest) Low-vulnerability zone

  20. The proposedframework

  21. Take home messages Complimentarityof resilience and vulnerability The notion of low-vulnerabilitykernelgeneralizesthat of viabilitykernel. Resilienceis the ability to get back to thissafety set after a disturbance or a change. Vulnerabilityis a statisticbased on the harm values associated to the possible trajectories. Choice of the strategydependent on the indicator.

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