Optimization of consensus time by combining the voter and the majority voter models on scale-free networksJae-Suk Yang1, In-mook Kim1 and Wooseop Kwak2
1 Department of Physics, Korea University - Seoul 136-713, Korea
2 Department of Physics, Chosun University - Gwangju 501-759, Korea
received 20 April 2009; accepted in final form 7 October 2009; published October 2009
published online 6 November 2009
We introduce a spin model combining the majority voter model with probability p and the voter model with probability 1-p and then measure its consensus time on scale-free networks with various degree exponents . We find that consensus time depends on both p and . When all spins follow either the voter model or the majority voter model, it takes much greater time to reach consensus. On the other hand, when spins may alternate between the majority voter model and the voter model, consensus time is shortened. We find via numerical calculation that the optimized ratio to minimize consensus time is around p = 0.72.
05.10.Ln - Monte Carlo methods.
89.75.-k - Complex systems.
89.75.Hc - Networks and genealogical trees.
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