From lakes and glades to viability algorithms: Automatic classification of system states according to the Topology of Sustainable Management


The framework Topology of Sustainable Management by Heitzig et al. (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.

European Physical Journal
Finn Müller-Hansen
Finn Müller-Hansen

Finn Müller-Hansen works in the group “Applied Sustainability Science” (APSIS) on applications of machine learning and bibliometric analysis on the scientific literature and public as well as political discourse about energy transitions. He is interested in methods from complex systems theory to investigate the interplay of social, economic, and ecological factors in transformations towards a sustainable economy.