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Journal Article

Survivability of deterministic dynamical systems

Authors
/persons/resource/frank.hellmann

Hellmann,  Frank
Potsdam Institute for Climate Impact Research;

/persons/resource/Paul.Schultz

Schultz,  Paul
Potsdam Institute for Climate Impact Research;

/persons/resource/grabow.carsten

Grabow,  Carsten
Potsdam Institute for Climate Impact Research;

/persons/resource/heitzig

Heitzig,  Jobst
Potsdam Institute for Climate Impact Research;

/persons/resource/Juergen.Kurths

Kurths,  Jürgen
Potsdam Institute for Climate Impact Research;

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Citation

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


Cite as: https://publications.pik-potsdam.de/pubman/item/item_21199
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.