Voter Model with Time dependent Flip-rates

Abstract

We introduce time variation in the flip-rates of the Voter Model. This type of generalisation is relevant to models of ageing in language change, allowing the representation of changes in speakers' learning rates over their lifetime and may be applied to any other similar model in which interaction rates at the microscopic level change with time. 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 time scale 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 to reach consensus for different states are very different. An opinion originally held by the fastest changing agents has a smaller chance to succeed, and takes much longer to do so than an evenly distributed opinion.

16 pages, 6 figures

References in corpus (9)

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• Heterogeneous Voter Models
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Cited by in corpus (9)

• Temporal networks: slowing down diffusion by long lasting interactions
• Dynamics of social balance under temporal interaction
• Competition in the presence of aging: order, disorder, and synchronized collective behavior
• Reduction from non-Markovian to Markovian dynamics: The case of aging in the noisy-voter model
• Timing interactions in social simulations: The voter model
• Accelerating coordination in temporal networks by engineering the link order
• Epidemics in networks: A master equation approach
• Fast fixation without fast networks
• Mean First Passage Time of the Symmetric Noisy Voter Model with Arbitrary Initial and Boundary Conditions