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  Survivability of deterministic dynamical systems

Hellmann, F., Schultz, P., Grabow, C., Heitzig, J., Kurths, J. (2016): Survivability of deterministic dynamical systems. - Scientific Reports, 6, 29654.
https://doi.org/10.1038/srep29654

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 Creators:
Hellmann, Frank1, Author              
Schultz, Paul1, Author              
Grabow, Carsten1, Author              
Heitzig, Jobst1, Author              
Kurths, Jürgen1, Author              
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1Potsdam Institute for Climate Impact Research, ou_persistent13              

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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.

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 Dates: 2016
 Publication Status: Finally published
 Pages: -
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 Rev. Type: Peer
 Identifiers: DOI: 10.1038/srep29654
PIKDOMAIN: Transdisciplinary Concepts & Methods - Research Domain IV
eDoc: 7359
Research topic keyword: Complex Networks
Research topic keyword: Energy
Research topic keyword: Nonlinear Dynamics
Organisational keyword: RD4 - Complexity Science
Working Group: Dynamics, stability and resilience of complex hybrid infrastructure networks
 Degree: -

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Title: Scientific Reports
Source Genre: Journal, SCI, Scopus, p3, OA
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Pages: - Volume / Issue: 6 Sequence Number: 29654 Start / End Page: - Identifier: CoNE: https://publications.pik-potsdam.de/cone/journals/resource/journals2_395