Abstract.
In this paper networks that optimize a combined measure of local and global synchronizability are evolved. It is shown that for low coupling improvements in the local synchronizability dominate network evolution. This leads to an expressed grouping of elements with similar native frequency into cliques, allowing for an early onset of synchronization, but rendering full synchronization hard to achieve. In contrast, for large coupling the network evolution is governed by improvements towards full synchronization, preventing any expressed community structure. Such networks exhibit strong coupling between dissimilar oscillators. Albeit a rapid transition to full synchronization is achieved, the onset of synchronization is delayed in comparison to the first type of networks. The paper illustrates that an early onset of synchronization (which relates to clustering) and global synchronization are conflicting demands on network topology.
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References
A.T. Winfree, The Geometry of Biological Time (Springer-Verlag, New York, 1980)
I. Blekhman, Synchronization in Science and Technology (ASME Press, New York, 1988)
S.C. Manrubia, A.S. Mikhailov, D.H. Zanette, Emergence of Dynamical Order. Synchronization Phenomena in Complex Systems (World Scientific, Singapore, 2004)
A. Pluchino, V. Latora, A. Rapisarda, Eur. Phys. J. B 50, 169 (2006)
Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, New York, 1984)
L.M. Pecora, T.L. Carroll, Phys. Rev. Lett. 80, 2109 (1998)
Z. Liu, Y.-C. Lai, F.C. Hoppensteadt, Phys. Rev. E 63, 055201 (2001)
M. Barahona, L.M. Pecora, Phys. Rev. Lett. 89, 054101 (2002)
T. Nishikawa et al., Phys. Rev. Lett. 91, 014101 (2003)
H. Hong et al., Phys. Rev. E 69, 067105 (2004)
Y. Moreno, A.F. Pacheco, Europhys. Lett. 68, 603 (2004)
D.-U. Hwang et al., Phys. Rev. Lett. 94, 138701 (2005)
J.G. Restrepo, E. Ott, B.R. Hunt, Phys. Rev. E 71, 036151 (2005)
A.E. Motter, C.S. Zhou, J. Kurths, Europhys. Lett. 69, 334 (2005)
D.-S. Lee, Phys. Rev. E 72, 026208 (2005)
M. Chavez et al., Phys. Rev. Lett. 94, 218701 (2005)
L. Donetti, P.I. Hurtado, M.A. Mu\(\tilde{\rm n}\)oz, Phys. Rev. Lett. 95, 188701 (2005)
C.S. Zhou, A.E. Motter, J. Kurths, Phys. Rev. Lett. 96, 034101 (2006)
D. Newth, M. Brede, Complex Systems 16, 317 (2006)
P.M. Gleiser, D.H. Zanette, Eur. Phys. J. B 53, 233 (2006)
G. Korniss, Phys. Rev. E 75, 051121 (2007)
C. Zhou, J. Kurths, Chaos 16, 015104 (2006)
J. Gómez-Gardenes, Y. Moreno, A. Arenas, Phys. Rev. Lett. 98, 034101 (2007)
J. Gómez-Gardenes, Y. Moreno, A. Arenas, Phys. Rev. E 75, 066106 (2007)
M. Brede, (2007) to appear in Phys. Lett. A, DOI: http://dx.doi.org/10.1016/j.physleta.2007.11.069
A. Arenas, A. Diaz-Guilera, C.J. Pérez-Vicente, Phys. Rev. Lett. 96, 114102 (2006)
S. Boccaletti, M. Ivanchenko, V. Latora, A. Pluchino, A. Rapisarda, Phys. Rev. E 75, (2007) 045102(R)
P. Erdös, A. Rényi, Publ. Math. Inst. Hung. Acad. Sci. Ser. A 5, 17 (1960)
D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998)
J.A. Almendral, A. Diaz-Guilera, New J. Phys. 9, 187 (2007)
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Brede, M. Locals vs. global synchronization in networks of non-identical Kuramoto oscillators. Eur. Phys. J. B 62, 87–94 (2008). https://doi.org/10.1140/epjb/e2008-00126-9
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DOI: https://doi.org/10.1140/epjb/e2008-00126-9