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

Autor(es)

Kittel, Tim ^[1] ; Mueller-Hansen, Finn ^{[1, 2]} ; Koch, Rebekka ^[3] ; Heitzig, Jobst ^[1] ; Deffuant, Guillaume ^[4] ; Mathias, Jean-Denis ^[4] ; Kurths, Juergen ^{[5, 1, 6]}

Afiliação do(s) autor(es)

^[1] Potsdam Inst Climate Impact Res PIK, Leibniz Assoc, POB 60 12 03, D-14412 Potsdam - Germany

^[2] Mercator Res Inst Global Commons & Climate Change, EUREF Campus 19, Torgauer Str 12-15, D-10829 Berlin - Germany

^[3] Univ Amsterdam, Inst Theoret Phys ITFA, Sci Pk 904, NL-1098 XH Amsterdam - Netherlands

^[4] Univ Clermont Auvergne, UR LISC, INRAE, Aubiere - France

^[5] Humboldt Univ, Inst Phys, Newtonstr 15, D-12489 Berlin - Germany

^[6] Lobachevsky Univ Nizhny Novgorod, Nizhnii Novgorod 603950 - Russia

• Tipo de documento: Artigo Científico
• Fonte: European Physical Journal-Special Topics; v. 230, n. 14-15 SEP 2021.
• Citações Web of Science: 1

Resumo

The framework Topology of Sustainable Management by Heitzig et al. (Earth Syst Dyn 7:21. , 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. (AU)

• Processo FAPESP: 11/50151-0 - Fenômenos dinâmicos em redes complexas: fundamentos e aplicações
• Beneficiário: Elbert Einstein Nehrer Macau
• Modalidade de apoio: Auxílio à Pesquisa - Temático