论文标题
虚拟步行灵感来自卑鄙的田野动力学交换模型的意见动态模型
Virtual walks inspired by a mean field kinetic exchange model of opinion dynamics
论文作者
论文摘要
我们提出了两种不同的方案，以实现与动力学动态动力学交换模型相对应的虚拟步行。散步本质上是马尔可夫人，要么是非马克维亚人。意见动力学模型的特征是参数$ p $，该参数以关键值$ p_c $驱动订单障碍过渡。位移的分销$ s（x，t）$从步行者的起源中$ x $进行计算。在$ p_c $以下，检测到与跨界行为相关的两个时间尺度，以不同的指数值的临界方式以幂律方式差异。 $ s（x，t）$还带有相变的签名，因为它以$ p_c $更改其表格。步行示出了$ p_c $以下的有偏见的随机步行的功能，并且在$ p_c $上方，步行就像无偏的随机步行。偏见以$ p_c $的力量方式消失，而由此产生的高斯功能的宽度显示出不连续性。步行的某些特征被认为与与平均字段模型相关的临界数量可媲美，该类别动力学模型所属的班级。马尔可夫和非马克维亚步行的结果几乎是相同的，这是通过考虑不同的通量来证明的。我们将目前的结果与一些早期的类似研究进行了比较。
We propose two different schemes of realizing a virtual walk corresponding to a kinetic exchange model of opinion dynamics. The walks are either Markovian or non-Markovian in nature. The opinion dynamics model is characterized by a parameter $p$ which drives an order disorder transition at a critical value $p_c$. The distribution $S(X,t)$ of the displacements $X$ from the origin of the walkers is computed at different times. Below $p_c$, two time scales associated with a crossover behavior in time are detected, which diverge in a power law manner at criticality with different exponent values. $S(X,t)$ also carries the signature of the phase transition as it changes its form at $p_c$. The walks show the features of a biased random walk below $p_c$, and above $p_c$, the walks are like unbiased random walks. The bias vanishes in a power law manner at $p_c$ and the width of the resulting Gaussian function shows a discontinuity. Some of the features of the walks are argued to be comparable to the critical quantities associated with the mean field Ising model, to which class the opinion dynamics model belongs. The results for the Markovian and non-Markovian walks are almost identical which is justified by considering the different fluxes. We compare the present results with some earlier similar studies.
