Pineda M.,IFISC Institute Fisica Interdisciplinar y Sistemas Complejos CSIC UIB |
Imbihl R.,Leibniz University of Hanover |
Schimansky-Geier L.,Humboldt University of Berlin
Physica A: Statistical Mechanics and its Applications | Year: 2010
The impact of surface size on two minimalistic models for the bistable CO oxidation is analytically studied. A simple model for the catalytic CO oxidation on nanoscale surfaces is analyzed by the chemical master equation. The analytical results predict a shift of the bistable region and cusp point in the global bifurcation diagram as a function of surface size. A reaction-diffusion stochastic model consisting of a collection of reactive subdomains locally coupled by CO diffusion is also considered. A local description of fluctuations can be obtained after applying a Weiss-type mean-field approximation. This approximation predicts, for infinitely many subdomains, a break of ergodicity and a bifurcation behavior like in first-order phase transitions as a function of surface size and coupling parameter. Analytical results are compared with Gillespie-type Monte Carlo simulations. © 2009 Elsevier B.V. All rights reserved.
Gonzalez-Avella J.C.,Federal University of Rio Grande do Sul |
Gonzalez-Avella J.C.,Instituto Nacional Of Ciencia E Tecnologia Of Sistemas Complexos |
Cosenza M.G.,University of Los Andes, Venezuela |
San Miguel M.,IFISC Institute Fisica Interdisciplinar y Sistemas Complejos CSIC UIB
Physica A: Statistical Mechanics and its Applications | Year: 2014
We investigate the emergence of localized coherent behavior in systems consisting of two populations of social agents possessing a condition for non-interacting states, mutually coupled through global interaction fields. We employ two examples of such dynamics: (i) Axelrod's model for social influence, and (ii) a discrete version of a bounded confidence model for opinion formation. In each case, the global interaction fields correspond to the statistical mode of the states of the agents in each population. In both systems we find localized coherent states for some values of parameters, consisting of one population in a homogeneous state and the other in a disordered state. This situation can be considered as a social analogue to a chimera state arising in two interacting populations of oscillators. In addition, other asymptotic collective behaviors appear in both systems depending on parameter values: a common homogeneous state, where both populations reach the same state; different homogeneous states, where both population reach homogeneous states different from each other; and a disordered state, where both populations reach inhomogeneous states. © 2013 Elsevier B.V. All rights reserved.
Grabowicz P.A.,IFISC Institute Fisica Interdisciplinar y Sistemas Complejos CSIC UIB |
Eguiluz V.M.,IFISC Institute Fisica Interdisciplinar y Sistemas Complejos CSIC UIB
EPL | Year: 2012
Many complex systems are characterized by broad distributions capturing, for example, the size of firms, the population of cities or the degree distribution of complex networks. Typically this feature is explained by means of a preferential growth mechanism. Although heterogeneity is expected to play a role in the evolution, it is usually not considered in the modeling probably due to a lack of empirical evidence on how it is distributed. We characterize the intrinsic heterogeneity of groups in an online community and then show that together with a simple linear growth and an inhomogeneous birth rate it explains the broad distribution of group members. © 2012 Europhysics Letters Association.