A generalized voter model with time-decaying memory on a multilayer   network
  By incorporating a multilayer network and time-decaying memory into the original voter model, the coupled effects of spatial and temporal cumulation of peer pressure on consensus are investigated. Heterogeneity in peer pressure and time-decaying mechanism are both found to be detrimental to consensus. The transition points, below which a consensus can always be reached and above which two opposed opinions are more likely to coexist, are found. A mean-field analysis indicates that the phase transitions in the present model are governed by the cumulative influence of peer pressure and the updating threshold. A functional relation between the consensus threshold and the decaying rate of the influence of peer pressure is found. As to the time to reach a consensus, it is governed by the coupling of the memory length and the decaying rate. An intermediate decaying rate may lead to much lower time to reach a consensus. 
Li-Xin Zhong, Wen-Juan Xu, Rong-Da Chen, Chen-Yang Zhong, Tian Qiu,   Yong-Dong Shi, Li-Liang Wang
physics.soc-ph