Operationalization of Topology of Sustainable Management to Estimate Qualitatively Different Regions in State Space

Tim Kittel (1) , Finn Müller-Hansen (1) , Rebekka Koch (1) , Jobst Heitzig (1) , Guillaume Deffuant (2) , Jean-Denis Mathias (2) , Jürgen Kurths (1)

1 PIK - Potsdam Institute for Climate Impact Research
2 UR LISC - Laboratoire d'ingénierie pour les systèmes complexes

To apply the framework Topology of Sustainable Management (tsm) by Heitzig et al. (2016) to dynamical models, we connect it to viability theory via a variant definition of the former. This enables us to use the Saint-Pierre algorithm to estimate the main partition of tsm. Furthermore, we present an extension of the algorithm to compute implicitly defined capture basins, regions of state space as defined in viability theory. We use a low-complexity model coupling environmental and socioeconomic dynamics to demonstrate the applicability of this approach. With this example, we highlight how common problems in estimations of these regions like (i) an unbounded state space and (ii) highly varying time scales can be circumvented by introducing appropriate coordinate transformations. The article thus shows how al-gorithmic approaches from viability theory can be used to get a better understanding of the state space of manageable dynamical systems. [TODO Jobst: incorporate newer refs in intro, ref to Felix, go through earlier reviewer comments and response.] [TODO J-D: update refs to viability papers?] [TODO all: update contact details, thanks and funding info in acknowledgements]

Domaines: Mathématiques [math]

Tim Kittel, Finn Müller-Hansen, Rebekka Koch, Jobst Heitzig, Guillaume Deffuant, et al.. Operationalization of Topology of Sustainable Management to Estimate Qualitatively Different Regions in State Space. 2020. ⟨hal-02961471⟩