Stability threshold approach for complex dynamical systems

Vladimir V. Klinshov, Vladimir I. Nekorkin, Jürgen Kurths

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A new measure to characterize the stability of complex dynamical systems against large perturbations is suggested, the stability threshold (ST). It quantifies the magnitude of the weakest perturbation capable of disrupting the system and switch it to an undesired dynamical regime. In the phase space, the ST 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 ST 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 the robustness of complex systems is studied.
Original languageEnglish
Article number013004
JournalNew Journal of Physics
Early online date21 Dec 2015
Publication statusPublished - Jan 2016

Bibliographical note

This paper was developed within the scope of the IRTG 1740/TRP 2011/50151-0, funded by the DFG/FAPESP, and supported by the Government of the Russian Federation (Agreement No. 14.Z50.31.0033 with the Institute of Applied Physics RAS). The first author thanks Dr Roman Ovsyannikov for valuable discussions regarding estimation of the mistake probability.


  • dynamical systems
  • attraction basin
  • nonlinear dynamics
  • basin stability


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