Survivability of Deterministic Dynamical Systems

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

50 Citations (Scopus)
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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
Publication statusPublished - 13 Jul 2016

Bibliographical note

We acknowledge gratefully the support of BMBF, CoNDyNet, FK. 03SF0472A, of the EIT Climate-KIC project SWIPO and Nora Molkenthin for illustrating our illustration of the concept of survivability using penguins. We thank Martin Rohden for providing us with the UK high-voltage transmission grid topology and Yang Tang for very useful discussions. The publication of this article was funded by the Open Access Fund of the Leibniz Association.


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