Digital.CSIC >
Ciencia y Tecnologías Físicas >
Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC) >
(IFISC) Artículos >
Open Access item Conservation laws for voterlike models on random directed networks 
Authors:  Serrano, M. Ángeles Klemm, Konstantin Vázquez, Federico Eguíluz, Víctor M. San Miguel, Maxi 
Issue Date:  30Sep2009 
Publisher:  Institute of Physics Publishing 
Citation:  Journal of Statistical Mechanics: Theory and Experiment: P10024 (2009) 
Abstract:  We study the voter model, under node and link update, and the related invasion process on a single strongly connected component of a directed network. We implement an analytical treatment in the thermodynamic limit using the heterogeneous meanfield assumption. From the dynamical rules at the microscopic level, we find the equations for the evolution of the relative densities of nodes in a given state on heterogeneous networks with arbitrary degree distribution and degree degree correlations. We prove that conserved quantities as weighted linear superpositions of spin states exist for all three processes and, for uncorrelated directed networks, we derive their specific expressions. We also discuss the time evolution of the relative densities that decay exponentially to a homogeneous stationary value given by the conserved quantity. The conservation laws obtained in the thermodynamic limit for a system that does not order in that limit determine the probabilities of reaching the absorbing state for a finite system. The contribution of each degree class to the conserved quantity is determined by a local property. Depending on the dynamics, the highest contribution is associated with influential nodes reaching a large number of outgoing neighbors, not too influenceable ones with a low number of incoming connections, or both at the same time. 
Description:  18 pages, 2 figures, 1 table. ArXiv preprint: http://arxiv.org/abs/arXiv:0902.1769 
Publisher version (URL):  http://dx.doi.org/10.1088/17425468/2009/10/P10024 
URI:  http://hdl.handle.net/10261/25513 
ISSN:  17425468 
???metadata.dc.identifier.doi???:  10.1088/17425468/2009/10/P10024 
Appears in Collections:  (IFISC) Artículos

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.
