Complex Systems

This research line is related to the study of complex systems in general, that are, systems composed by many interacting units whose collective behavior cannot be inferred from the individual behavior of their units.  In particular, our work is focused on the study of social systems that exhibit emergent properties at large scales, such as coordination, synchronization and consensus.  We propose simple models of interacting agents that attempt to reproduce simple aspects of different collective phenomena observed in various social and economic dynamics, including the competition for human resources, opinion formation, disease spreading, the dissemination of culture and the competition between languages, among others.  Some of the models we implement are the minority game for the dynamics of resources, the voter model and the majority rule model for opinion dynamics, the contact process and the susceptible-infected-susceptible model for diseases, the Axelrod model for cultural formation and the Abrams-Strogatz model for language dynamics.

These systems are studied by means of numerical simulations and various techniques borrowed from non-equilibrium statistical physics, such as master equations, Langevin equations, the theory of phase transitions and mean-field theoretical approximations.  A fundamental tool used in our studies are complex networks, which have shown in the last years to be very useful at describing the interactions observed in complex systems of various scientific disciplines (biochemical, protein, neural and social networks).