Journal
NEW JOURNAL OF PHYSICS
Volume 20, Issue -, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1367-2630/aab5e6
Keywords
dynamical systems; networks; basin stability
Categories
Funding
- Government of the Russian Federation [14.Z50.31.0033]
- Government of the Russian Federation (Institute of Applied Physics RAS)
- Russian Science Foundation [14-12-01358]
- Russian Science Foundation [17-12-00066, 14-12-01358] Funding Source: Russian Science Foundation
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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 maybe 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.
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