Regensburg 2016 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 30: Poster - Complex nonlinear systems
DY 30.14: Poster
Dienstag, 8. März 2016, 18:15–21:00, Poster C
Survivability: How Undesired Transients Affect The Stability of Dynamical Systems — Paul Schultz1,2, •Frank Hellmann1, Carsten Grabow1, Jobst Heitzig1, and Jürgen Kurths1,2,3,4 — 1Potsdam Institute for Climate Impact Research, P.O. Box 60 12 03, 14412 Potsdam, Germany — 2Department of Physics, Humboldt University of Berlin, Newtonstr. 15, 12489 Berlin, Germany — 3nstitute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom — 4Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, 606950 Nizhny Novgorod, Russia
The notion of a part of phase space containing desired/allowed states of a dynamical system is important in a wide range of complex systems research. It has been called safe operating space, viability kernel or sunny region. Here we define survivability: Given a random initial condition, what is the likelihood that the transient behaviour of a deterministic system leaves the region of desirable states? In conceptual examples we show that this basic measure captures notions of fundamental for interest various systems, e.g. climate models or power grids. We also derive a semi-analytic lower bound for the survivability of linear systems with polygonal safe operating space. We then apply the concept in the case the power grid model in realistic operating regimes to assess our analytic bound. Here, the kind of stability measured by survivability is of great practical interest. Furthermore, it is not captured by stability measures based on asymptotic trajectories.