Abstract
In this paper we construct and analyse strongly connected sparse directed networks with an enhanced propensity for synchronization (PFS). Two types of PFS-enhanced networks are considered: (i) an eigenratio minimizing ensemble with non-vanishing complex parts of the spectrum and (ii) a class of networks with real spectrum but slightly larger eigenratios than (i). We relate the superior PFSs to a strongly skewed out-degree distribution, the density of double links and a hierarchical periphery-core organization. Ensembles (i) and (ii) are found to differ in the density of double links and the particular organization of the core and the periphery-core linkage.
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A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, C. Zhou, Phys. Rep. 469, 93 (2008)
R. Albert, A.-L. Barábasi, Rev. Mod. Phys. 74, 47 (2002)
M.E.J. Newman, SIAM Rev. 45, 167 (2003)
S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Phys. Rep. 424, 175 (2006)
L.M. Pecora, T.L. Carroll, Phys. Rev. Lett. 80, 2109 (1998)
M. Timme, Europhys. Lett. 76, 367 (2006)
M. Brede, Phys. Lett. A 372, 5305 (2008)
M. Brede, Europhys. Lett. 84, 40004 (2008)
A.E. Motter, C. Zhou, J. Kurths, Phys. Rev. E 71, 016116 (2005)
M. Zhao, T. Zhou, B.-H. Wang, G. Yan, H.-J. Yang, W.-J. Bai, Physica A 371, 773 (2006)
M. Brede, Eur. Phys. J. B 62, 87 (2008)
M. Brede, Phys. Lett. A 372, 2618 (2008)
M.di Bernardo, F. Garofalo, F. Sorrentino, Int. J. Bifurcat. Chaos 17, 3499 (2007)
D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998)
T. Nishikawa, A.E. Motter, Y.-C. Lai, F.C. Hoppensteadt, Phys. Rev. Lett. 91, 014101 (2003)
H. Hong, B.J. Kim, M.Y. Choi, H. Park, Phys. Rev. E 69, 067105 (2004)
F.M. Atay, T. Biyikoglu, J. Jost, Physica D 224, 35 (2006)
A.E. Motter, C.S. Zhou, J. Kurths, Europhys. Lett. 69, 334 (2005)
D.-U. Hwang, M. Chavez, A. Amann, S. Boccaletti, Phys. Rev. Lett. 94, 138701 (2005)
M. Chavez, D.-U. Hwang, A. Amann, H.G.E. Hentschel, S. Boccaletti, Phys. Rev. Lett. 94, 218701 (2005)
L. Donetti, P.I. Hurtado, M.A. Muñoz, Phys. Rev. Lett. 95, 188701 (2005)
R.V. Sole, R. Ferrer i Cancho, in Lecture Notes in Physics 625 (Springer, Berlin, 2003)
V. Colizza, J.R. Banavar, A. Maritan, A. Rinaldo, Phys. Rev. Lett. 92, 198701 (2004)
E.A. Variano, J.H. McCoy, H. Lipson, Phys. Rev. Lett. 92, 188701 (2004)
J. Ash, D. Newth, Physica A 380, 673 (2007)
K.S. Fink, G. Johnson, C. Carroll, D. Mar, L. Pecora, Phys. Rev. E 61, 5080 (2000)
H.J. Sommers, A. Crisanti, H. Somplinsky, Y. Stein, Phys. Rev. Lett. 60, 1895 (1988)
I. Lodato, S. Boccaletti, V. Latora, Europhys. Lett. 78, 28001 (2007)
Y. Moreno, M. Vazquez-Prada, A.F. Pacheco, Physica A 343, 279 (2004)
We also experimented with different cut-offs and made sure that the presented results are robust with regard to the specific choice
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Brede, M. Optimal synchronization on strongly connected directed networks. Eur. Phys. J. B 74, 217–225 (2010). https://doi.org/10.1140/epjb/e2010-00016-7
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DOI: https://doi.org/10.1140/epjb/e2010-00016-7