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A Spectral Approach to Synchronizability of Interdependent Networks

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Nonlinear Phenomena in Complex Systems: From Nano to Macro Scale

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Abstract

The quality of life in full developed countries depends on the cooperative functioning of different infrastructures. One of the most striking problems is to understand in simple terms to what extent this cooperation can be assured. The complexity science provides a powerful means to analyze the interaction of such critical infrastructures at pure topological level. The application of the paradigm of complexity to the global system resulting from the interdependent infrastructures leads to the concept of “Network of Networks”. The present work is devoted to understand emergent (that is collective) synchronization behaviors through the spectral analysis of the laplacian. We provide evidence that, upon increasing the number of links between the different infrastructures, the behavior of the total system experiences a drastic changes in its synchronization modes. When few links are introduced, the synchronization inside the component networks is very fast and the global synchronization takes place mainly at the boundaries; on the other side, when the number of links exceeds a threshold, the bottlenecks for the synchronization process localize mainly inside the component networks.

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Acknowledgements

We thank Javier Martin Hernandez, Huijuan Wang and Piet Van Mieghem for their significant and useful suggestions. Interesting discussions with Antonio De Nicola, Antonio Scala and Gene Stanley are also acknowledged. This work was partly supported by the European project MOTIA (Grant JLS-2009-CIPS-AG-C1-016), Prevention, Preparedness and Consequence Management of Terrorism and other Security-related Risks Program European Commission – Directorate-General Home Affairs. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

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Authors and Affiliations

  1. ENEA – CR Casaccia, via Anguillarese, 301 – 00123, Roma, Italy

    Gregorio D’Agostino

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  1. Gregorio D’Agostino
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Correspondence to Gregorio D’Agostino .

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Editors and Affiliations

  1. Turin Polytechnic University in Tashkent, Tashkent, Uzbekistan

    Davron Matrasulov

  2. Department of Physics, Boston University, Boston, Massachusetts, USA

    H. Eugene Stanley

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D’Agostino, G. (2014). A Spectral Approach to Synchronizability of Interdependent Networks. In: Matrasulov, D., Stanley, H. (eds) Nonlinear Phenomena in Complex Systems: From Nano to Macro Scale. NATO Science for Peace and Security Series C: Environmental Security. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8704-8_9

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  • DOI: https://doi.org/10.1007/978-94-017-8704-8_9

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-017-8703-1

  • Online ISBN: 978-94-017-8704-8

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