Dresden 2017 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 43: Nonlinear Dynamics, Synchronizsation and Chaos
DY 43.11: Vortrag
Donnerstag, 23. März 2017, 12:15–12:30, ZEU 118
Finite Time Basin Stability and Basin Escape Rates — •Paul Schultz1,2, Frank Hellmann1, Kevin Webster1, and Jürgen Kurths1,2,3,4 — 1Potsdam Institute for Climate Impact Research, P.O. Box 601203, 14412 Potsdam, Germany — 2Department of Physics, Humboldt University of Berlin, Newtonstr. 15, 12489 Berlin, Germany — 3Institute 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
We define the finite-time basin stability, which is the probability of a system returning closely enough to an equilibrium within a certain time while being subject to random shocks at specified time intervals.
When the frequency of these perturbations becomes low enough for the system to equilibrate between two shocks, subsequent perturbations are independent and the measure yields the conventional basin stability (Menck et al. Nat. Phys. 9, 89-92. 2013).
Using an appropriately defined Lyapunov function, we show that finite-time basin stability reveals information about the maximum frequency of perturbations at which basin stability becomes the escape rate from the basin. As an example, we use Kuramoto oscillators with inertia.