A voter model with time dependent flip rates

作者：Baxter G J^*

来源：Journal of Statistical Mechanics: Theory and Experiment , 2011, P09005.

DOI：10.1088/1742-5468/2011/09/P09005

• population dynamics (theory)
• interacting agent models
• stochastic processes

We introduce time variation in the flip rates of the voter model. This type of generalization may be applied to other diffusion-like models in which interaction rates at the microscopic level may change with time, for example in models of language change, allowing the representation of changes in speakers' learning rates over their lifetime. The mean time taken to reach consensus varies in a nontrivial way with the rate of change of the flip rates, varying between bounds given by the mean consensus times for static homogeneous (the original voter model) and static heterogeneous flip rates. By considering the mean time between interactions for each agent, we derive excellent estimates of the mean consensus times and exit probabilities for any timescale of flip rate variation. The scaling of consensus times with population size on complex networks is correctly predicted, and is as would be expected for the ordinary voter model. Heterogeneity in the initial distribution of opinions has a strong effect, considerably reducing the mean time to consensus, while increasing the probability of survival of the opinion which initially occupies the most slowly changing agents. The mean times taken to reach consensus for different states are very different. An opinion originally held by the fastest changing agents has a smaller chance of succeeding, and takes much longer to do so than an evenly distributed opinion.

• 出版日期2011-9