Abstract
Complexity, a century-old problem with seemingly endless possibilities, has driven scientists from all disciplines within Natural and Computing Sciences to test the limits of their paradigms and theories, eventually, bringing them together in the hope of creating a new paradigm that could shed light into the Complexity problems. One of the most intensely scrutinised problems in this emerging cross- and inter-disciplinary Science of Complexity, is to determine the mathematical principles and underlying mechanisms that give rise to the emergence of collective behaviour in complex systems, namely, systems that are composed by many interacting units or sub-systems (Fig. 1.1). Researchers across the world have turned their attention into finding the minimal set of variables and conditions that one needs to explain and predict these collective behaviour, which emerge without the need for any central control or external driving force, namely, they self-organise.
Humanity needs practical men, who get the most out of their work, and, without forgetting the general good, safeguard their own interests. But humanity also needs dreamers, for whom the disinterested development of an enterprise is so captivating that it becomes impossible for them to devote their care or to their own material profit.
Without doubt, these dreamers do not deserve wealth, because they do not desire it. Even so, a well-organized society should assure to such workers the efficient means of accomplishing their task, in a life freed from material care and freely consecrated to research.
Taken from the book by Eve Curie (translated by Vincent Sheean), Madame Curie, Pocket books, Simon and Schuster, New York, 352–353 (1946).
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S. Milgram, “The Small World Problem”, Psychology Today 2 (1967), pp. 60–67.
References
A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2003)
S. Strogatz, Sync: The Emerging Science of Spontaneous Order (Hyperion, New York, 2003)
S.C. Manrubia, A.S. Mikhailov, D.H. Zanette, Emergence of Dynamical Order Synchronization Phenomena in Complex Systems (World Scientific, Singapore, 2004)
A.R. Bergen, D.J. Hill, A structure preserving model for power system stability analysis. IEEE Trans. Power Appl. Syst. 100, 25–35 (1981)
J.A. Acebrón, L.L. Bonilla, C.J. Pérez Vicente, F. Ritort, R. Spigler, The Kuramoto model: a simple paradigm for synchronization phenomena. Rev. Mod. Phys. 77, 137–185 (2005)
M. Perrin, G.L. Lippi, A. Politi, Phase transition in a radiation-matter interaction with recoil and collisions. Phys. Rev. Lett. 86(20), 4520 (2001)
N. Rubido, C. Grebogi, M.S. Baptista, Structure and function in flow networks. Europhys. Lett. 101, 68001 (2013)
N. Rubido, C. Grebogi, M.S. Baptista, Resilient evolving supply-demand networks. Phys. Rev. E 89, 012801 (2014)
M.T. Brown, A picture is worth a thousand words: energy systems language and simulation. Ecol. Model. 178, 83–100 (2004)
E. Katifori, G.J. Szollosi, M.O. Magnasco, Damage and fluctuations induce loops in optimal transport networks. Phys. Rev. Lett. 104, 048704 (2010)
D. Hu, D. Cai, Adaptation and Optimization of Biological Transport Networks. Phys. Rev. Lett. 111, 138701 (2013)
G.G. Batrouni, A. Hansen, Fracture in three-dimensional fuse networks. Phys. Rev. Lett. 80(2), 325 (1998)
C.F.S. Pinheiro, A.T. Bernarde, Scale-free fuse network and its robustness. Phys. Rev. E 72, 046709 (2005)
F. Dörfler, F. Bullo, Spectral analysis of synchronization in a lossless structure-preserving power network model. IEEE Int. Conf. Smart GridCommun. 179–184 (2010)
Y. Susuki, I. Mezić, T. Hikihara, Global swing instability in the new england power grid model, in IEEE 2009 American Control Conference, (2009), pp. 3446–3451
Y. Susuki, I. Mezić, T. Hikihara, Coherent swing instability of power grids. J. Nonlinear Sci. 21, 403–439 (2011)
F. Pasqualetti, A. Bicchi, F. Bullo, A graph-theoretical characterization of power network vulnerabilities, in, IEEE 2011 American Control Conference, (2011), pp. 3918–3923
F. Dörfler, F. Bullo, Synchronization and transient stability in power networks and nonuniform Kuramoto oscillators. SIAM J. Control Opt. 50(3), 1616–1642 (2012)
F. Dörfler, M. Chertkov, F. Bullo, Synchronization in complex oscillator networks and smart grids. Proc. Natl. Acad. Sci. 110(6), 2005–2010 (2013)
G.A. Pagani, M. Aiello, The power grid as a complex network: a survey. Physica A 392, 2688–2700 (2013)
G.A. Pagani, M. Aiello, Power grid complex network evolutions for the smart grid. Physica A 396, 248–266 (2014)
P.H.J. Nardelli, N. Rubido, C. Wang, M.S. Baptista, C. Pomalaza-Raez, P. Cardieri, M. Latva-aho, Models for the modern power-grid. Eur. Phys. J. Spec. Top. 10, 1–15 (2014)
G. Kron, A set of principles to interconnect the solutions of physical systems. J. Appl. Phys. 24(8), 965–980 (1953)
F. Dörfler, F. Bullo, Kron reduction of graphs with applications to electrical networks. IEEE Trans. Circ. Syst. I: Regul. Pap. 60(1), 150–163 (2013)
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Rubido, N. (2016). Introduction. In: Energy Transmission and Synchronization in Complex Networks. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-22216-5_1
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