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

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

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 Creators:
Kittel, Tim1, Author              
Müller-Hansen, Finn1, Author              
Koch, Rebekka2, Author
Heitzig, Jobst1, Author              
Deffuant, Guillaume2, Author
Mathias, Jean-Denis2, Author
Kurths, Jürgen1, Author              
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1Potsdam Institute for Climate Impact Research, ou_persistent13              
2External Organizations, ou_persistent22              

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 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.

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 Dates: 2021-09-132021-09-13
 Publication Status: Finally published
 Pages: -
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 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1140/epjs/s11734-021-00262-2
MDB-ID: yes - 3257
PIKDOMAIN: RD4 - Complexity Science
Organisational keyword: RD4 - Complexity Science
Research topic keyword: Complex Networks
Research topic keyword: Nonlinear Dynamics
Research topic keyword: Sustainable Development
Research topic keyword: Planetary Boundaries
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Title: European Physical Journal - Special Topics
Source Genre: Journal, SCI, Scopus, p3
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Pages: - Volume / Issue: 230 (14-15) Sequence Number: - Start / End Page: 3133 - 3152 Identifier: CoNE: https://publications.pik-potsdam.de/cone/journals/resource/150617
Publisher: Springer