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Synchronization of complex networks. (English) Zbl 1155.93034
Caponetto, Riccardo (ed.) et al., Advanced topics on cellular self-organizing nets and chaotic nonlinear dynamics to model and control complex systems. Hackensack, NJ: World Scientific (ISBN 978-981-281-404-3/hbk). World Scientific Series on Nonlinear Science. Series A 63, 123-157 (2008).
Introduction: During the last decades the emergence of collective dynamics in large networks of coupled units has been investigated in many different areas of science. In particular, the effect of synchronization in systems of coupled oscillators nowadays provides a unifying framework for phenomena arising in fields such as optics, chemistry, biology and ecology (for recent reviews see [A. Pikovsky, M. Rosenblum and J. Kurths, Synchronization: a universal concept in nonlinear sciences, Cambridge: Cambridge University Press (2001; Zbl 0993.37002), S. Boccaletti, J. Kurths, D. L. Valladares, G. Osipov and C. S. Zhou, Phys. Rep. 366, No. 1–2, 1–101 (2002; Zbl 0995.37022), S. Manrubia, A. S. Mikhailov and A. H. Zanette, Emergence of dynamical order, Hackensack, NJ: World Scientific (2004; Zbl 1119.34001)]). Recently, complex networks have provided a challenging framework for the study of synchronization of dynamical units, based on the interplay between complexity in the overall topology and local dynamical properties of the coupled units [S. H. Strogatz, exploring complex networks, Nature 410, 268 (2001); S. Boccaletti, V. Latora, Y. Moreno, M. Chavez and D.-U. Hwang, complex networks: structure and dynamics, Phys. Rep. 424, 175 (2006)].
This chapter aims at reviewing the main techniques that have been proposed for assessing the propensity for synchronization (synchronizability) of a given networked system. We will describe the main applications, especially in the view of selecting the optimal topology in the coupling configuration that provides enhancement of the synchronization features.
For the entire collection see [Zbl 1148.37001].
93D15 Stabilization of systems by feedback
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
93A15 Large-scale systems
93D99 Stability of control systems
90B10 Deterministic network models in operations research