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Dynamics of a Repulsive Voter Model

In contrast to most conventional social interaction models, in this paper, the dynamics of repulsive interactions between the nodes of a network is investigated. Such a model may be considered to be a first-order approximation of many anticonformal social policies, such as drivers making lane-changing decisions when confronted with other cars in the same lane. Such policies are also demonstrated in any sort of social situation where there is a premium on novelty or choices, which can demonstrate an attitude of indifference or rebellion toward current trends. Various styles of antifashionable dresses, which are explicitly contrary to the fashion of the day, are the examples of such anticonformal social behavior. The model developed in this paper is first formulated and solved over a complete graph both with and without the influence of biased nodes. Monte Carlo simulations have been performed to validate the accuracy of the model formulation. Then, the model is studied on an Erdös Rényi random graph, and finally, the behavior of the model on a regular lattice is investigated. Analytical solutions have been derived for the mentioned combinations. The interesting behavior of the model regarding the dependence of the equilibrium distribution on population size, convergence time, and the effect of biased nodes is presented.