Key Words: Complex networked systems, synchronization phenomena, mathematical biology, epidemiology, spreading processes, evolutionary dynamics.
Participants: Yamir Moreno, Luís M. Floría, Jesús Gómez-Gardeñes, Sandro Meloni, Javier Borge-Holthoefer
Contact: Yamir Moreno and Mario Floría
Summary of the line:
Complex Networks are ubiquitous incontemporary sciences. Recent studies [Boccaletti2006] have demonstrated that systems as diverse as food chains, the World Wide Web (WWW), Internet, cellular, metabolic and protein networks, as well as many social systems, among others, share several topological properties. The main topological characteristics of these networks, such as its scale-free character and the small-world property [Strogatz2001,Boccaletti2006], have opened a promising field to the application of methods and concepts of Statistical Mechanics to the study of these systems. In this regard, the consideration of affinities, directionality and functionality of connections, along with the incorporation of archetypical nonlinear dynamics (activation-inhibition, cooperation-competition, etc…) will allow models to simulate more adequately the functioning of real networks and its use to design strategies addressed to specific goals. Besides, complex networks are interesting from a wider point of view: It is useful to represent the architecture of many complex systems as an interacting network. Therefore, the study of complex networks and the dynamical processes on them will to some extent open the door to the theory of complex systems, a promising line of research where much attention from the scientific community is increasingly paid.
Though many important advances in the study of structure and dynamics of complex networks have been made in the last years, there is still much to do, especially regarding the relation of the networks structure to their function, as well as the transfer of knowledge to practical applications. In the present proposal we intend to continue the group recent works on the field and to address new problems recently raised. The proposed tasks include the study of nonlinear dynamical processes coupled to complex topologies [Gomez2006b], with the goal of understanding how structure influences the functional organization and robustness of cellular nets, as well as models of synchronization [Gomez2007a,Gomez2007b,Gomez2007c] in complex networks in order to analyze when its architecture favors synchronization and error tolerance. Besides we will continue the study of general dynamical processes relevant in epidemiology [Hwang2005,Gomez2006a,Gomez2008] and communication networks [Echenique2004,Echenique2005a,Echenique2005b,Nekovee2006,Wang2006] in general. Finally, in the framework of this research line we will analyze the emergence of collective and cooperative behaviors in social systems through the implementation of different algorithms of evolutionary dynamics of cooperative and coordination games on graphs [Szabo2007,Gomez2007d,Poncela2007] and the modeling of synchronization phenomena relevant in social systems, to simulate the emergence of social consensus. Regarding methodological issues, both analytical and numerical approaches will be followed.
The previous works of the group in this field made it a national and international referent. Currently, the group maintains numerous collaborations with scientists from other national and abroad institutions: Alex Arenas (Univ Rovira i Virgili), Albert Díaz-Guilera (Univ. Barcelona), Ángel Sánchez (Univ. Carlos III), Stefano Bocaletti (Inst. Naz. Di Optica, Firenze), Vito Latora (Univ. de Catania), Maziar Nekovee (British Telecom y UCL, Londres, UK), and Jurgen Kurths (Univ. Postdam, Alemania). The project will benefit from these collaborations, which in turn will enhance the diffusion of our results and the international impact of our group
[Strogatz01] S.H. Strogatz . Nature 410, 268 (2001).
[Boccaletti2006] S. Boccaletti, V. Latora, Y. Moreno, M. Chávez, D.-U. Hwang, Phys. Rep. 424, 175-308 (2006)
[Echenique2004] P. Echenique, J. Gómez-Gardeñes, Y. Moreno. Phys. Rev. E 70, 056105 (2004)
[Echenique2005a] P.Echenique, J.Gómez Gardeñes, Y.Moreno and A.Vázquez. Physical Review E 71 035102(R)-1(4) (2005)
[Echenique2005b] P. Echenique, J. Gómez-Gardeñes and Y. Moreno. Europhysics Letters 71, 325 (2005).
[Hwang2005] D.-U. Hwang, S. Boccaletti, Y.Moreno, and R. Lopez-Ruiz Mathematical Biosciences and Engineering 2, 317-27 (2005)
[Gomez2006a] J. Gómez-Gardeñes, P. Echenique and Y. Moreno. European Physical Journal B 49, 259 (2006)
[Wang2006] F. Wang, Y. Moreno, Y. Sun. Phys. Rev. E 73, 036123 (2006)
[Gomez2007a] J. Gómez-Gardeñes, Y. Moreno, A. Arenas. Phys. Rev. Lett 98, 034101 (2007)
[Gomez2007b] J. Gómez-Gardeñes, Y. Moreno, A. Arenas. Phys. Rev. E 75, 066106 (2007)
[Gomez2007c] J. Gómez-Gardeñes, Y. Moreno. Int. J. Bif. Chaos (Focus Issue), 17, 2501-2507 (2007)
[Gomez2006b] J. Gómez-Gardeñes, Y. Moreno and L.M. Floría. Chaos 16, 15114 (2006)
[Gomez2007d] J. Gómez-Gardeñes, M. Campillo, L.M. Floría and Y. Moreno. Phys. Rev. Lett. 98, 108103 (2007)
[Poncela2007] J. Poncela, J. Gómez-Gardeñes, L.M. Floría, Y. Moreno. New J. Phys. 9, 184 (2007)
[Gomez2008] J. Gómez-Gardeñes, V. Latora, Y. Moreno, E. Profumo. Proc. Natl. Acad. Sci. USA, in press (2008)
[Szabo2007] G. Szabo and G. Fath. Phys. Rep. 446, 97-216 (2007)
