Survivability of Deterministic Dynamical Systems
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.
Cite
@article{arxiv.1506.01257,
title = {Survivability of Deterministic Dynamical Systems},
author = {Frank Hellmann and Paul Schultz and Carsten Grabow and Jobst Heitzig and Jürgen Kurths},
journal= {arXiv preprint arXiv:1506.01257},
year = {2016}
}
Comments
21 pages, 6 figures