# Which Mathematical Formalizations of Resilience and What For?

### Workshop, Montpellier,8 October 2013

The workshop, organized by Guillaume Deffuant, Jean-Denis Mathias and Catherine Calvayrac (Irstea – LISC), was held **On October 8, 2013, from 9:00 to 17:00**, in **hotel Oceania, ** 3 rue du Clos René, Montpellier.

### Program:

09:00–09:15 | Introduction to the workshop (Guillaume Deffuant) |

09:15–10:00 | Marty Anderies , the School of Sustainability, Arizona State University |

10:00–10:45 | Olivier Barreteau , Irstea Montpellier |

11:15–12:00 | Steven Lade , Stockholm Resilience Center |

12:00–12:45 | Luc Doyen, CNRS, Paris^{1} |

14:00–14:30 | Sophie Martin , Irstea Clermont-Ferrand |

14:30–15:00 | Bruno Bonté , Irstea Montpellier |

15:00–15:30 | Charles Rougé , Irstea Clermont-Ferrand |

16:00–17:00 | Discussion panel with invited speakers |

^{1} Please request directly the presentation to Luc Doyen if interested.

### Scope:

This workshop is part of a workshop series in preparation for the 2014 Resilience Conference to be held in Montpellier, France. The objective of the workshop series was to bring together French and international scientific communities for an in-depth exploration of the multiple dimensions of resilience following the theme of the 2014 Resilience Conference: *“Adaptation, Transformation and Development”.*

This specific workshop focused on the different trends of research on mathematical formalizations of resilience and on their practical use. Indeed, the mathematics of resilience generally relates resilience with the attractors of the system’s dynamics and proposes different means for qualifying the tendency of the system to return to a desired attractor after a perturbation. This approach is hence based on a study of the system’s attractors and attractor basins, with the tipping points corresponding to the boundaries between attractor basins. Recently, Viability Theory has been proposed as a conceptual and practical tool for formalizing resilience. The proponents of this approach claim that it generalizes the attractor based ones and that it can include more explicitly the search for efficient action policies and express rigorously the adaptability of a system.

### Synthesis of the final discussion

The following points were emphasized by the invited speakers:

- Formalizing resilience is often useful and sometimes necessary but the current trend in the Resilience Alliance privileges qualitative and practical approaches, so the communication about mathematical developments towards this community is difficult,
- It is important to keep a plurality of viewpoints when formalizing resilience because some viewpoints can be more adapted to some problems or stakeholders,
- An interest of the viability framework is to distinguish clearly between different scientific problems: modelling the dynamics of the system, defining the constraints, deriving the action policies that fit the constraints. Each problem shows specific difficulties:
- Modelling dynamics shows usual problems of modelling (availability of expertise, of data, integrating scales, evaluating uncertainties, robustness of the model, etc…). Modelling social dynamics is particularly difficult and often leads to high uncertainties, especially when collective behaviours emerge from individual rules. In the viability framework these difficulties are considered independent from the definition of resilience per se (whereas in other views of resilience, specificities of social dynamics such as agency, empowerment, adaptation should be included in the definition of resilience),
- Defining the constraints is generally seen as a political problem, about which scientists can give an insight by computing possible consequences of different choices of constraints. In some cases, one can imagine to model the evolution of the constraints as a social process. This is a social dynamics which is very difficult to model but that could be integrated into the framework (by adding the time as an explicit state dimension in order to deploy evolving constraints).
- Computing viable or resilient action policies with current methods is often heavy and even intractable when the dimension of the state space is large, especially when computing viability kernels or resilience basins. This problem relates to the scientific field of robust control.

- The whole viability framework of resilience should be the subject of experiments. These experiments may target very limited, well controlled parts of the viability framework, or the process globally on real or fake case studies. This would open new research questions that seem promising.

### Follow-up actions

- Organizing a session at Resilience 2014 on the topic of the workshop,
- Different groups of researchers participating to the workshop will submit projects about: experiments, methodological problems
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