5 results
Search Results
Now showing 1 - 5 of 5
- ItemInterval stability for complex systems(Bristol : Institute of Physics Publishing, 2018) Klinshov, V.V.; Kirillov, S.; Kurths, J.; Nekorkin, V.I.Stability of dynamical systems against strong perturbations is an important problem of nonlinear dynamics relevant to many applications in various areas. Here, we develop a novel concept of interval stability, referring to the behavior of the perturbed system during a finite time interval. Based on this concept, we suggest new measures of stability, namely interval basin stability (IBS) and interval stability threshold (IST). IBS characterizes the likelihood that the perturbed system returns to the stable regime (attractor) in a given time. IST provides the minimal magnitude of the perturbation capable to disrupt the stable regime for a given interval of time. The suggested measures provide important information about the system susceptibility to external perturbations which may be useful for practical applications. Moreover, from a theoretical viewpoint the interval stability measures are shown to bridge the gap between linear and asymptotic stability. We also suggest numerical algorithms for quantification of the interval stability characteristics and demonstrate their potential for several dynamical systems of various nature, such as power grids and neural networks.
- ItemStability threshold approach for complex dynamical systems(Bristol : Institute of Physics Publishing, 2016) Klinshov, V.V.; Nekorkin, V.I.; Kurths, J.
- ItemExperiments on the magnetorotational instability in helical magnetic fields(College Park, MD : Institute of Physics Publishing, 2007) Stefani, F.; Gundrum, T.; Gerbeth, G.; Rüdiger, G.; Szklarski, J.; Hollerbach, R.The magnetorotational instability (MRI) plays a key role in the formation of stars and black holes, by enabling outward angular momentum transport in accretion discs. The use of combined axial and azimuthal magnetic fields allows the investigation of this effect in liquid metal flows at moderate Reynolds and Hartmann numbers. A variety of experimental results is presented showing evidence for the occurrence of the MRI in a Taylor-Couette flow using the liquid metal alloy GaInSn. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
- ItemDetours around basin stability in power networks(Bristol : Institute of Physics Publishing, 2014) Schultz, P.; Heitzig, J.; Kurths, J.To analyse the relationship between stability against large perturbations and topological properties of a power transmission grid, we employ a statistical analysis of a large ensemble of synthetic power grids, looking for significant statistical relationships between the single-node basin stability measure and classical as well as tailormade weighted network characteristics. This method enables us to predict poor values of single-node basin stability for a large extent of the nodes, offering a node-wise stability estimation at low computational cost. Further, we analyse the particular function of certain network motifs to promote or degrade the stability of the system. Here we uncover the impact of so-called detour motifs on the appearance of nodes with a poor stability score and discuss the implications for power grid design.
- ItemPotentials and limits to basin stability estimation(Bristol : Institute of Physics Publishing, 2017) Schultz, P.; Menck, P.J.; Heitzig, J.; Kurths, J.Stability assessment methods for dynamical systems have recently been complemented by basin stability and derived measures, i.e. probabilistic statements whether systems remain in a basin of attraction given a distribution of perturbations. Their application requires numerical estimation via Monte Carlo sampling and integration of differential equations. Here, we analyse the applicability of basin stability to systems with basin geometries that are challenging for this numerical method, having fractal basin boundaries and riddled or intermingled basins of attraction. We find that numerical basin stability estimation is still meaningful for fractal boundaries but reaches its limits for riddled basins with holes.