Numerical analysis of the rebellious voter model

Abstract

The rebellious voter model, introduced by Sturm and Swart (2008), is a variation of the standard, one-dimensional voter model, in which types that are locally in the minority have an advantage. It is related, both through duality and through the evolution of its interfaces, to a system of branching annihilating random walks that is believed to belong to the `parity-conservation' universality class. This paper presents numerical data for the rebellious voter model and for a closely related one-sided version of the model. Both models appear to exhibit a phase transition between noncoexistence and coexistence as the advantage for minority types is increased. For the one-sided model (but not for the original, two-sided rebellious voter model), it appears that the critical point is exactly a half and two important functions of the process are given by simple, explicit formulas, a fact for which we have no explanation.

Compared to last version, only minor changes in Figure 10. 26 pages. 20 figures. A black and white version of the manuscript and the raw data and variables plotted in the figures are available from the homepage of the first author

References in corpus (6)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Non-perturbative fixed point in a non-equilibrium phase transition
• Coexistence in locally regulated competing populations and survival of branching annihilating random walk
• Critical behavior of an even offspringed branching and annihilating random walk cellular automaton with spatial disorder
• Voter models with heterozygosity selection
• Cluster mean-field study of the parity conserving phase transition

Cited by in corpus (3)

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• Phase transition in a double branching annihilating random walk