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Stability threshold approach for complex dynamical systems

Authors
  • Klinshov, Vladimir V.
  • Nekorkin, Vladimir I.
  • Kurths, Jürgen
Type
Preprint
Publication Date
Dec 11, 2015
Submission Date
Apr 17, 2015
Identifiers
DOI: 10.1088/1367-2630/18/1/013004
Source
arXiv
License
Yellow
External links

Abstract

A new measure to characterize stability of complex dynamical systems against large perturbation is suggested, the stability threshold (ST). It quantifies the magnitude of the weakest perturbation capable to disrupt the system and switch it to an undesired dynamical regime. In the phase space, the stability threshold corresponds to the "thinnest site" of the attraction basin and therefore indicates the most "dangerous" direction of perturbations. We introduce a computational algorithm for quantification of the stability threshold and demonstrate that the suggested approach is effective and provides important insights. The generality of the obtained results defines their vast potential for application in such fields as engineering, neuroscience, power grids, Earth science and many others where robustness of complex systems is studied.

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