Stability threshold approach for complex dynamical systems

Acknowledgments This paper was developed within the scope of the IRTG 1740/TRP 2011/50151-0, funded by the DFG/FAPESP, and supported by the Government of the Russian Federation (Agreement No. 14.Z50.31.0033 with the Institute of Applied Physics RAS). The first author thanks Dr Roman Ovsyannikov for valuable discussions regarding estimation of the mistake probability.

Survivability : A Unifiying Concept for the Transient Resilience of Deterministic Dynamical Systems

16 pages

Survivability : A Unifiying Concept for the Transient Resilience of Deterministic Dynamical Systems

16 pages

Data Based Identification and Prediction of Nonlinear and Complex Dynamical Systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.

Survivability of Deterministic Dynamical Systems

Acknowledgements 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.