The European Physical Journal B

, Volume 67, Issue 3, pp 301–318

Nonlinear voter models: the transition from invasion to coexistence


    • Chair of Systems Design, ETH Zurich, Kreuzplatz 5
  • L. Behera
    • Department of Electrical EngineeringIndian Institute of Technology
Interdisciplinary Physics Regular Article

DOI: 10.1140/epjb/e2009-00001-3

Cite this article as:
Schweitzer, F. & Behera, L. Eur. Phys. J. B (2009) 67: 301. doi:10.1140/epjb/e2009-00001-3


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.


87.23.Cc Population dynamics and ecological pattern formation87.23.Ge Dynamics of social systems
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© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009