Nonlinear Voter Models: The Transition from Invasion to Coexistence

dc.creatorSchweitzer, Frank
dc.creatorBehera, Laxmidhar
dc.date2003-07-30
dc.date2008-12-13
dc.date.accessioned2026-07-07T12:59:52Z
dc.date.available2026-07-07T12:59:52Z
dc.descriptionIn nonlinear voter models the transitions between two states depend in a nonlinear manner on the frequencies of these states in the neighborhood. We investigate the role of these nonlinearities on the global outcome of the dynamics for a homogeneous network where each node is connected to $m=4$ neighbors. The paper unfolds in two directions. We first develop a general stochastic framework for frequency dependent processes from which we derive the macroscopic dynamics for key variables, such as global frequencies and correlations. Explicite expressions for both the mean-field limit and the pair approximation are obtained. We then apply these equations to determine a phase diagram in the parameter space that distinguishes between different dynamic regimes. The pair approximation allows us to identify three regimes for nonlinear voter models: (i) complete invasion, (ii) random coexistence, and -- most interestingly -- (iii) correlated coexistence. These findings are contrasted with predictions from the mean-field phase diagram and are confirmed by extensive computer simulations of the microscopic dynamics.
dc.descriptionCompletely revised and extended version, new results and interpretation. 39 pages, 24 figures. European Physical Journal B, vol 67 (2009)
dc.identifierhttps://arxiv.org/abs/cond-mat/0307742
dc.identifierhttp://arxiv.org/abs/cond-mat/0307742
dc.identifierEuropean Physical Journal B, vol 67 (2009) 301-318
dc.identifierdoi:10.1140/epjb/e2009-00001-3
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/225705
dc.subjectStatistical Mechanics
dc.subjectPattern Formation and Solitons
dc.subjectPhysics and Society
dc.subjectPopulations and Evolution
dc.titleNonlinear Voter Models: The Transition from Invasion to Coexistence
dc.typetext

Files

Collections