Deciphering the imprint of topology on nonlinear dynamical network stability

Acknowledgments The authors gratefully acknowledge the support of BMBF, CoNDyNet, FK. 03SF0472A. The authors gratefully acknowledge the European Regional Development Fund (ERDF), the German Federal Ministry of Education and Research and the Land Brandenburg for supporting this project by providing resources on the high performance computer system at the Potsdam Institute for Climate Impact Research. The publication of this article was funded by the Open Access Fund of the Leibniz Association. We further thank Peng Ji for helpful discussions regarding the interpretation of the results.

[1]  David J. Hill,et al.  Power systems as dynamic networks , 2006, 2006 IEEE International Symposium on Circuits and Systems.

[2]  Jürgen Kurths,et al.  Local vs. global redundancy – trade-offs between resilience against cascading failures and frequency stability , 2016, The European Physical Journal Special Topics.

[3]  Jürgen Kurths,et al.  An integrative quantifier of multistability in complex systems based on ecological resilience , 2015, Scientific Reports.

[4]  Michael Chertkov,et al.  Synchronization in complex oscillator networks and smart grids , 2012, Proceedings of the National Academy of Sciences.

[5]  Jean-Pierre Aubin,et al.  Viability Theory: New Directions , 2011 .

[6]  M. Hasler,et al.  Connection Graph Stability Method for Synchronized Coupled Chaotic Systems , 2004 .

[7]  K. R. Padiyar,et al.  Power system dynamics : stability and control , 1996 .

[8]  M. Timme,et al.  Critical Links and Nonlocal Rerouting in Complex Supply Networks. , 2015, Physical review letters.

[9]  Edgar Knobloch,et al.  Transient spatio-temporal chaos in the complex Ginzburg–Landau equation on long domains , 2010 .

[10]  Albert-László Barabási,et al.  Universal resilience patterns in complex networks , 2016, Nature.

[11]  G. Filatrella,et al.  Analysis of a power grid using a Kuramoto-like model , 2007, 0705.1305.

[12]  K. Webster,et al.  Timing of transients: quantifying reaching times and transient behavior in complex systems , 2016, 1611.07565.

[13]  Janusz Bialek,et al.  Power System Dynamics: Stability and Control , 2008 .

[14]  Jurgen Kurths,et al.  A random growth model for power grids and other spatially embedded infrastructure networks , 2014, The European Physical Journal Special Topics.

[15]  Peter J. Menck,et al.  How basin stability complements the linear-stability paradigm , 2013, Nature Physics.

[16]  Y. Lai,et al.  Data Based Identification and Prediction of Nonlinear and Complex Dynamical Systems , 2016, 1704.08764.

[17]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[18]  Jürgen Kurths,et al.  Detours around basin stability in power networks , 2014 .

[19]  S. Olmi.  Chimera states in coupled Kuramoto oscillators with inertia. , 2015, Chaos.

[20]  A. Vespignani,et al.  The architecture of complex weighted networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Adilson E Motter,et al.  Heterogeneity in oscillator networks: are smaller worlds easier to synchronize? , 2003, Physical review letters.

[22]  Mauricio Barahona,et al.  Synchronization in small-world systems. , 2002, Physical review letters.

[23]  Michael T. Gastner,et al.  The complex network of global cargo ship movements , 2010, Journal of The Royal Society Interface.

[24]  Jobst Heitzig,et al.  Potentials and limits to basin stability estimation , 2016, 1603.01844.

[25]  Ian Dobson,et al.  Synchrony and your morning coffee , 2013, Nature Physics.

[26]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[27]  C. Folke.  RESILIENCE: THE EMERGENCE OF A PERSPECTIVE FOR SOCIAL-ECOLOGICAL SYSTEMS ANALYSES , 2006 .

[28]  Joachim Peinke,et al.  Self-organized synchronization and voltage stability in networks of synchronous machines , 2013, ArXiv.

[29]  Jurgen Kurths,et al.  The impact of model detail on power grid resilience measures , 2015, 1510.05640.

[30]  C. S. Holling.  Resilience and Stability of Ecological Systems , 1973 .

[31]  Eckehard Schöll,et al.  Transient scaling and resurgence of chimera states in networks of Boolean phase oscillators. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  K. H. Lee,et al.  The statistical mechanics of complex signaling networks: nerve growth factor signaling , 2004, Physical biology.

[33]  Hildegard Meyer-Ortmanns,et al.  Synchronization of Rössler oscillators on scale-free topologies , 2006 .

[34]  Simona Olmi,et al.  Hysteretic transitions in the Kuramoto model with inertia. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Adilson E. Motter,et al.  Comparative analysis of existing models for power-grid synchronization , 2015, 1501.06926.

[36]  J. Peinke,et al.  Turbulent character of wind energy. , 2013, Physical review letters.

[37]  Ke Sun,et al.  Complex Networks Theory: A New Method of Research in Power Grid , 2005, 2005 IEEE/PES Transmission & Distribution Conference & Exposition: Asia and Pacific.

[38]  Marc Timme,et al.  Self-organized synchronization in decentralized power grids. , 2012, Physical review letters.

[39]  Santosh S. Vempala,et al.  Simulated annealing in convex bodies and an O*(n4) volume algorithm , 2006, J. Comput. Syst. Sci..

[40]  Thomas K. D. M. Peron,et al.  The Kuramoto model in complex networks , 2015, 1511.07139.

[41]  Ying-Cheng Lai,et al.  Transient Chaos: Complex Dynamics on Finite Time Scales , 2011 .

[42]  Jobst Heitzig,et al.  How dead ends undermine power grid stability , 2014, Nature Communications.

[43]  R. Spigler,et al.  The Kuramoto model: A simple paradigm for synchronization phenomena , 2005 .

[44]  T. Carroll,et al.  Master Stability Functions for Synchronized Coupled Systems , 1998 .

[45]  Erik M. Bollt,et al.  Master stability functions for coupled nearly identical dynamical systems , 2008, 0811.0649.

[46]  Jean-Pierre Aubin.  Viability Kernels and Capture Basins of Sets Under Differential Inclusions , 2001, SIAM J. Control. Optim..

[47]  E. Lorenz,et al.  Short term fluctuations of wind and solar power systems , 2016, 1606.03426.