Survivability of Deterministic Dynamical Systems

Frank Hellmann, Paul Schultz, Carsten Grabow, Jobst Heitzig, Jürgen Kurths

Research output: Contribution to journalArticle

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Abstract

The notion of a part of phase space containing desired (or allowed) states of a dynamical system is important in a wide range of complex systems research. It has been called the safe operating space, the viability kernel or the sunny region. In this paper we define the notion of survivability: Given a random initial condition, what is the likelihood that the transient behaviour of a deterministic system does not leave a region of desirable states. We demonstrate the utility of this novel stability measure by considering models from climate science, neuronal networks and power grids. We also show that a semi-analytic lower bound for the survivability of linear systems allows a numerically very efficient survivability analysis in realistic models of power grids. Our numerical and semi-analytic work underlines that the type of stability measured by survivability is not captured by common asymptotic stability measures.

Original languageEnglish
Article number29654
Pages (from-to)1-12
Number of pages12
JournalScientific Reports
Volume6
DOIs
Publication statusPublished - 13 Jul 2016

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Dynamical systems
Asymptotic stability
Linear systems
Large scale systems

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Hellmann, F., Schultz, P., Grabow, C., Heitzig, J., & Kurths, J. (2016). Survivability of Deterministic Dynamical Systems. Scientific Reports, 6, 1-12. [29654]. https://doi.org/10.1038/srep29654

Survivability of Deterministic Dynamical Systems. / Hellmann, Frank; Schultz, Paul; Grabow, Carsten; Heitzig, Jobst; Kurths, Jürgen.

In: Scientific Reports, Vol. 6, 29654, 13.07.2016, p. 1-12.

Research output: Contribution to journalArticle

Hellmann, F, Schultz, P, Grabow, C, Heitzig, J & Kurths, J 2016, 'Survivability of Deterministic Dynamical Systems' Scientific Reports, vol. 6, 29654, pp. 1-12. https://doi.org/10.1038/srep29654
Hellmann F, Schultz P, Grabow C, Heitzig J, Kurths J. Survivability of Deterministic Dynamical Systems. Scientific Reports. 2016 Jul 13;6:1-12. 29654. https://doi.org/10.1038/srep29654
Hellmann, Frank ; Schultz, Paul ; Grabow, Carsten ; Heitzig, Jobst ; Kurths, Jürgen. / Survivability of Deterministic Dynamical Systems. In: Scientific Reports. 2016 ; Vol. 6. pp. 1-12.
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