CC BY 4.0 UnportedHellmann, FrankSchultz, PaulGrabow, CarstenHeitzig, JobstKurths, Jürgen2016-07-152019-06-282016https://doi.org/10.34657/392https://oa.tib.eu/renate/handle/123456789/3878The 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.application/pdfenghttps://creativecommons.org/licenses/by/4.0/500Complex networksNonlinear phenomenaArticle