Operationalization of Topology of Sustainable Management to Estimate Qualitatively Different Regions in State Space
To apply the framework of Topology of Sustainable Management (TSM) by Heitzig et al. (2016) to dynamical models, we connect it to viability theory (VT) via a variant definition of the former. This enables us to use the Saint-Pierre algorithm to estimate the main partition of TSM, improving the operationalization of TSM. Furthermore, we present an extension of the algorithm to compute implicitly defined capture basins, a notion from VT that is more elaborated in the article, as these come up in TSM. We use a low- complexity model coupling environmental and socio-economic dynamics to demonstrate the applicability of this approach. Two common problems of estimations in VT are critical for this example: (i) an unbounded state space and (ii) highly varying time scales. We solve both by introducing appropriate coordinate transformations. These solutions are applicable for general systems, too.
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