The European Physical Journal B

, Volume 67, Issue 3, pp 301–318

Nonlinear voter models: the transition from invasion to coexistence

Interdisciplinary Physics Regular Article

Abstract

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. 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 from the mean-field phase diagram and are confirmed by extensive computer simulations of the microscopic dynamics.

PACS

87.23.Cc Population dynamics and ecological pattern formation 87.23.Ge Dynamics of social systems 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Chair of Systems Design, ETH Zurich, Kreuzplatz 5ZurichSwitzerland
  2. 2.Department of Electrical EngineeringIndian Institute of TechnologyKanpurIndia

Personalised recommendations