Nonlinear Voter Models: The Transition from Invasion to Coexistence
| dc.creator | Schweitzer, Frank | |
| dc.creator | Behera, Laxmidhar | |
| dc.date | 2003-07-30 | |
| dc.date | 2008-12-13 | |
| dc.date.accessioned | 2026-07-07T12:59:52Z | |
| dc.date.available | 2026-07-07T12:59:52Z | |
| dc.description | In 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.description | Completely revised and extended version, new results and interpretation. 39 pages, 24 figures. European Physical Journal B, vol 67 (2009) | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0307742 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0307742 | |
| dc.identifier | European Physical Journal B, vol 67 (2009) 301-318 | |
| dc.identifier | doi:10.1140/epjb/e2009-00001-3 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225705 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Pattern Formation and Solitons | |
| dc.subject | Physics and Society | |
| dc.subject | Populations and Evolution | |
| dc.title | Nonlinear Voter Models: The Transition from Invasion to Coexistence | |
| dc.type | text |