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Klinshov et al 2018, Interval stability for complex systems.pdf1,42 MBAdobe PDFView/Open
Title: Interval stability for complex systems
Authors: Klinshov, V.V.Kirillov, S.Kurths, J.Nekorkin, V.I.
Publishers Version: https://doi.org/10.1088/1367-2630/aab5e6
Issue Date: 2018
Published in: New Journal of Physics Vol. 20 (2018), No. 4
Publisher: Bristol : Institute of Physics Publishing
Abstract: 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.
Keywords: basin stability; dynamical systems; networks; Asymptotic stability; Dynamical systems; Electric power transmission networks; Large scale systems; Networks (circuits); External perturbations; Finite time intervals; Numerical algorithms; Perturbed systems; Stability of dynamical systems; Stability thresholds; Strong perturbations; System susceptibility; System stability
DDC: 530
License: CC BY 3.0 Unported
Link to License: https://creativecommons.org/licenses/by/3.0/
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