Nonlinear voter models: the transition from invasion to coexistence

F Schweitzer, Laxmidhar Behera

    Research output: Contribution to journalArticlepeer-review

    45 Citations (Scopus)

    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 languageEnglish
    Pages (from-to)301-318
    JournalEuropean Physical Journal B: Condensed Matter and Complex Systems
    Volume67
    Issue number3
    DOIs
    Publication statusPublished - 2009

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    Keywords

    • Population dynamics and ecological pattern formation
    • Dynamics of social
    • systems

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