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Author: Grabow, Carsten × End date: 2019 × Start date: 2016 × DDC: 500 × Type: article × Version: publishedVersion × Publisher: London : Nature Publishing Group ×

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    Survivability of deterministic dynamical systems
    (London : Nature Publishing Group, 2016) Hellmann, Frank; Schultz, Paul; Grabow, Carsten; Heitzig, Jobst; Kurths, Jürgen
    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.