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From lakes and glades to viability algorithms: automatic classification of system states according to the topology of sustainable management

Authors
/persons/resource/tim.kittel

Kittel,  Tim
Potsdam Institute for Climate Impact Research;

/persons/resource/mhansen

Müller-Hansen,  Finn
Potsdam Institute for Climate Impact Research;

Koch,  Rebekka
External Organizations;

/persons/resource/heitzig

Heitzig,  Jobst
Potsdam Institute for Climate Impact Research;

Deffuant,  Guillaume
External Organizations;

Mathias,  Jean-Denis
External Organizations;

/persons/resource/Juergen.Kurths

Kurths,  Jürgen
Potsdam Institute for Climate Impact Research;

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Citation

Kittel, T., Müller-Hansen, F., Koch, R., Heitzig, J., Deffuant, G., Mathias, J.-D., Kurths, J. (2021): From lakes and glades to viability algorithms: automatic classification of system states according to the topology of sustainable management. - European Physical Journal - Special Topics, 230, 14-15, 3133-3152.
https://doi.org/10.1140/epjs/s11734-021-00262-2


Cite as: https://publications.pik-potsdam.de/pubman/item/item_26324
Abstract
The framework Topology of Sustainable Management by Heitzig et al. (Earth Syst Dyn 7:21. https://doi.org/10.5194/esd-7-21-2016, 2016) distinguishes qualitatively different regions in state space of dynamical models representing manageable systems with default dynamics. In this paper, we connect the framework to viability theory by defining its main components based on viability kernels and capture basins. This enables us to use the Saint-Pierre algorithm to visualize the shape and calculate the volume of the main partition of the Topology of Sustainable Management. We present an extension of the algorithm to compute implicitly defined capture basins. To demonstrate the applicability of our approach, we introduce a low-complexity model coupling environmental and socioeconomic dynamics. With this example, we also address two common estimation problems: an unbounded state space and highly varying time scales. We show that appropriate coordinate transformations can solve these problems. It is thus demonstrated how algorithmic approaches from viability theory can be used to get a better understanding of the state space of manageable dynamical systems.