Stability threshold approach for complex dynamical systems

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

Research output: Contribution to journalArticle

11 Citations (Scopus)
6 Downloads (Pure)

Abstract

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
Volume18
Early online date21 Dec 2015
DOIs
Publication statusPublished - Jan 2016

Fingerprint

dynamical systems
thresholds
perturbation
neurology
Earth sciences
disrupting
complex systems
attraction
grids
engineering

Keywords

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

Cite this

Stability threshold approach for complex dynamical systems. / Klinshov, Vladimir V.; Nekorkin, Vladimir I.; Kurths, Jürgen.

In: New Journal of Physics, Vol. 18, 013004, 01.2016.

Research output: Contribution to journalArticle

Klinshov, Vladimir V. ; Nekorkin, Vladimir I. ; Kurths, Jürgen. / Stability threshold approach for complex dynamical systems. In: New Journal of Physics. 2016 ; Vol. 18.
@article{c8a589dfb39b4382a34bb39169f285e1,
title = "Stability threshold approach for complex dynamical systems",
abstract = "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.",
keywords = "dynamical systems, attraction basin, nonlinear dynamics, basin stability",
author = "Klinshov, {Vladimir V.} and Nekorkin, {Vladimir I.} and J{\"u}rgen Kurths",
note = "Acknowledgments 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.",
year = "2016",
month = "1",
doi = "10.1088/1367-2630/18/1/013004",
language = "English",
volume = "18",
journal = "New Journal of Physics",
issn = "1367-2630",
publisher = "IOP Publishing Ltd.",

}

TY - JOUR

T1 - Stability threshold approach for complex dynamical systems

AU - Klinshov, Vladimir V.

AU - Nekorkin, Vladimir I.

AU - Kurths, Jürgen

N1 - Acknowledgments 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.

PY - 2016/1

Y1 - 2016/1

N2 - 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.

AB - 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.

KW - dynamical systems

KW - attraction basin

KW - nonlinear dynamics

KW - basin stability

U2 - 10.1088/1367-2630/18/1/013004

DO - 10.1088/1367-2630/18/1/013004

M3 - Article

VL - 18

JO - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

M1 - 013004

ER -