Zhang Weituo, Lim Chjan C, Korniss G, Szymanski Boleslaw K
Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY, 12180-3590 USA.
Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY, 12180-3590 USA.
Sci Rep. 2014 Jul 4;4:5568. doi: 10.1038/srep05568.
We investigate the two-word Naming Game on two-dimensional random geometric graphs. Studying this model advances our understanding of the spatial distribution and propagation of opinions in social dynamics. A main feature of this model is the spontaneous emergence of spatial structures called opinion domains which are geographic regions with clear boundaries within which all individuals share the same opinion. We provide the mean-field equation for the underlying dynamics and discuss several properties of the equation such as the stationary solutions and two-time-scale separation. For the evolution of the opinion domains we find that the opinion domain boundary propagates at a speed proportional to its curvature. Finally we investigate the impact of committed agents on opinion domains and find the scaling of consensus time.
我们研究二维随机几何图上的双词命名游戏。对该模型的研究有助于我们深入理解社会动态中观点的空间分布和传播。该模型的一个主要特征是自发出现被称为观点域的空间结构，观点域是具有清晰边界的地理区域，区域内所有个体持有相同观点。我们给出了基础动力学的平均场方程，并讨论了该方程的几个性质，如平稳解和双时间尺度分离。对于观点域的演化，我们发现观点域边界以与其曲率成正比的速度传播。最后，我们研究了坚定参与者对观点域的影响，并得出了达成共识时间的标度关系。
