Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:C1L-D

Session:

Number:598

The integration/segregation phenomena in evolving complex networks

Juan A. Almendral,  Vanesa Ávalos Gaytán,  Satu Elisa Schaeffer,  Stefano Boccaletti,  

pp.598-601

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.598

PDF download (337.9KB)

Summary:
We study the integration/segregation problem from the viewpoint of complex networks, but considering that the network topology is not static but there is an adaptive mechanism acting on the links. Our goal is to identify under which conditions network synchronization occurs and what structural properties are present in the network topology when this happens. In particular, we experimentally compute the main descriptive structural properties of the network when it has been modified with the proposed mechanism, and it is elucidated the relationship between these results and the observed synchronization at both the local and global scale. Our main finding is that modularity, a global feature, can naturally emerge in a network when evolving links are considered, that is, by means of dynamical properties at the local scale.

References:

[1] M. Girvan and M. E. J. Newman, “Community structure in social and biological networks”, Proc. Natl. Acad. Sci. USA 99, 7821, 2002.

[2] J. A. Almendral, R. Criado, I. Leyva, J. M. Buldú and I. Sendiña-Nadal, “Introduction to Focus Issue: Mesoscales in Complex Networks”, Chaos 21, 016101, 2011.

[3] J. Hui-Jun, W. Hao and H. Zhong-Huai, “Explosive Synchronization and Emergence of Assortativity on Adaptive Networks”, Chinese Physics Letters28, 056802, 2011.

[4] Y. Ishida and T. Hayashi, “Asymmetric Phenomena of Segregation and Integration in Biological Systems: A matching Automaton”, Lecture Notes in Computer Science 5712, 789, 2009.

[5] G. Tononi, O. Sporns and G. M. Edelman, “A complexity measure for selective matching of signals by the brain”, Proc. Natl. Acad. Sci. USA93, 3422, 1996.

[6] O. Sporns, D. Chialvo, M. Kaiser and C. C. Hilgetag, “Organization, development and function of complex brain networks”, Trends in Cognitive Sciences8, 418, 2004.

[7] J. A. Acebrón, L. L. Bonilla, C. J. Pérez Vicente, F. Ritort and R. Spigler, “The Kuramoto model: A simple paradigm for synchronization phenomena”, Reviews of Modern Physics 77(1), 137, 2005.

[8] Y. Kuramoto, “Self-entrainment of a population of coupled nonlinear oscillators”, Lecture Notes in Physics 39, 420, 1975.

[9] Y. Kuramoto, “Chemical Oscillations, Waves, and Turbulence”, Springer, New York, USA, 1984.

[10] M. E. J. Newman, “Modularity and community structure in networks”, Proc. Natl. Acad. Sci. USA 103, 8577, 2006.

[11] V. D. Blondel, J.-L. Guillaume, R. Lambiotte and E. Lefebvre, “Fast unfolding of communities in large networks”, Journal of Statistical Mechanics: Theory and Experiment 10, P10008, 2008.