Voter model with non-Poissonian inter-event intervals

Recent analysis of social communications among humans has revealed that the interval between interactions for a pair of individuals and for an individual often follows a long-tail distribution. We investigate the effect of such a non-Poissonian nature of human behavior on dynamics of opinion formation. We use a variant of the voter model and numerically compare the time to consensus of all the voters with different distributions of interevent intervals and different networks. Compared with the exponential distribution of interevent intervals (i.e., the standard voter model), the power-law distribution of interevent intervals slows down consensus on the ring. This is because of the memory effect; in the power-law case, the expected time until the next update event on a link is large if the link has not had an update event for a long time. On the complete graph, the consensus time in the power-law case is close to that in the exponential case. Regular graphs bridge these two results such that the slowing down of the consensus in the power-law case as compared to the exponential case is less pronounced as the degree increases.

[1]  E. Todeva.  Networks , 2007 .

[2]  Jari Saramäki,et al.  Small But Slow World: How Network Topology and Burstiness Slow Down Spreading , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Albert-László Barabási,et al.  The origin of bursts and heavy tails in human dynamics , 2005, Nature.

[4]  S. Redner,et al.  Voter models on heterogeneous networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Krzysztof Suchecki,et al.  Voter model dynamics in complex networks: Role of dimensionality, disorder, and degree distribution. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[7]  Brian Karrer,et al.  Message passing approach for general epidemic models. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  S Redner,et al.  Evolutionary dynamics on degree-heterogeneous graphs. , 2006, Physical review letters.

[9]  P. Clifford,et al.  A model for spatial conflict , 1973 .

[10]  A. Barabasi,et al.  Impact of non-Poissonian activity patterns on spreading processes. , 2006, Physical review letters.

[11]  Ciro Cattuto,et al.  What's in a crowd? Analysis of face-to-face behavioral networks , 2010, Journal of theoretical biology.

[12]  M. Newman,et al.  Random graphs with arbitrary degree distributions and their applications. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Jean-Pierre Eckmann,et al.  Entropy of dialogues creates coherent structures in e-mail traffic. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[14]  R. Holley,et al.  Ergodic Theorems for Weakly Interacting Infinite Systems and the Voter Model , 1975 .

[15]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .

[16]  J. T. Cox,et al.  Coalescing Random Walks and Voter Model Consensus Times on the Torus in $\mathbb{Z}^d$ , 1989 .

[17]  Ciro Cattuto,et al.  Dynamics of Person-to-Person Interactions from Distributed RFID Sensor Networks , 2010, PloS one.

[18]  V. Eguíluz,et al.  Update rules and interevent time distributions: slow ordering versus no ordering in the voter model. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Sidney Redner,et al.  A guide to first-passage processes , 2001 .

[20]  K. Pearson,et al.  Biometrika , 1902, The American Naturalist.

[21]  Alessandro Vespignani,et al.  Dynamical Processes on Complex Networks , 2008 .

[22]  S. Redner,et al.  Voter model on heterogeneous graphs. , 2004, Physical review letters.

[23]  Albert-László Barabási,et al.  Limits of Predictability in Human Mobility , 2010, Science.

[24]  S. Havlin,et al.  Scaling laws of human interaction activity , 2009, Proceedings of the National Academy of Sciences.

[25]  G. Madey,et al.  Uncovering individual and collective human dynamics from mobile phone records , 2007, 0710.2939.

[26]  V. Eguíluz,et al.  Conservation laws for the voter model in complex networks , 2004, cond-mat/0408101.

[27]  Adilson E. Motter,et al.  A Poissonian explanation for heavy tails in e-mail communication , 2008, Proceedings of the National Academy of Sciences.

[28]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[29]  Chris Arney,et al.  Networks, Crowds, and Markets: Reasoning about a Highly Connected World (Easley, D. and Kleinberg, J.; 2010) [Book Review] , 2013, IEEE Technology and Society Magazine.

[30]  J. Stoyanov.  A Guide to First‐passage Processes , 2003 .

[31]  S. Fortunato,et al.  Statistical physics of social dynamics , 2007, 0710.3256.

[32]  F. Schweitzer,et al.  Decelerating microdynamics can accelerate macrodynamics in the voter model. , 2007, Physical review letters.

[33]  F. Vazquez,et al.  Analytical solution of the voter model on uncorrelated networks , 2008, 0803.1686.

[34]  Esteban Moro,et al.  Impact of human activity patterns on the dynamics of information diffusion. , 2009, Physical review letters.

[35]  D. Parisi,et al.  Comparison of voter and Glauber ordering dynamics on networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Albert-László Barabási,et al.  Modeling bursts and heavy tails in human dynamics , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  K. Goh,et al.  Spreading dynamics following bursty human activity patterns. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  R. Hidalgo,et al.  Conditions for the emergence of scaling in the inter-event time of uncorrelated and seasonal systems , 2006 .