Abstract
In nonlinear voter models the transitions between two states depend in a nonlinear manneron 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. Explicit 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 fromthe mean-field phase diagram and are confirmed by extensive computer simulations of the microscopicdynamics.PACS. 87.23.Cc
| Original language | English |
|---|---|
| Pages (from-to) | 301-318 |
| Journal | European Physical Journal B: Condensed Matter and Complex Systems |
| Volume | 67 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published (in print/issue) - 2009 |
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Keywords
- Population dynamics and ecological pattern formation
- Dynamics of social
- systems