Berlin 2015 – scientific programme
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BP: Fachverband Biologische Physik
BP 48: Physics of Sustainability and Human-Nature Interactions II (joint SOE/DY/jDPG/BP/AKE)
BP 48.5: Talk
Thursday, March 19, 2015, 18:15–18:30, MA 001
Topology of Sustainable Management of Dynamical Systems with Desirable States — •Jobst Heitzig1 and Tim Kittel1,2 — 1Potsdam Institute for Climate Impact Research — 2Humboldt University Berlin
The sustainable management of systems mainly governed by an internal dynamics for which one desires to stay in a certain region of their state space requires an understanding of the topology of the system's state space in terms of what regions are ``safe'' to stay in, and to what qualitative degree, and which of these regions can be reached from which others by the internal dynamics or by management.
The paradigm of optimal control on the one hand does not provide sufficient concepts for such a qualitative analysis and on the other hand typically requires quite a lot of structural knowledge about the problem, in particular, some or other form of quantitative evaluation of states.
In this talk, we will derive in a purely topological way a thorough qualitative classification of the possible states and management options of a system with respect to the possibility of avoiding or leaving some given undesired region by means of some given management options. Our results indicate that the sustainable management of a system may require discrete decisions such as choosing between ultimate safety and permanent desirability, or between permanent safety and increasing future options, etc.