论文标题
具有极端开关和混乱的意见形成模型：批判行为和动态
Opinion formation models with extreme switches and disorder: critical behaviour and dynamics
论文作者
论文摘要
在三个州动力学交换舆论形成模型中，在最近的一篇论文中考虑了极端开关的效果。在目前的工作中，我们研究了相同的模型。这里的疾病意味着概率$ p $可能发生负相互作用。在没有极端开关的情况下，已知的临界点在平均场模型中为$ p_c = 1/4 $。由于$ q $的非零值表示此类开关的概率，因此发现关键点发生在$ p = \ frac {1-q} {4} {4} $中，其中订单参数随指数$β= 1/2 $的通用值而消失。对相边界附近最初有序状态的稳定性分析揭示了在有序/无序相位的订单参数的指数增长/衰减，并且时间尺度与指数$ 1 $不同。完全有序的状态还以相似的时间尺度的相似行为呈指数呈指数呈其平衡值。正好在关键点，订单参数显示了随时间的衰减，指数为$ 1/2 $。尽管关键行为仍然是卑鄙的字段，但该系统的行为更像是两个状态模型，如$ q \至1 $。在$ q = 1 $的情况下，模型的行为就像二进制选民模型，随机翻转概率$ p $。
In a three state kinetic exchange opinion formation model, the effect of extreme switches was considered in a recent paper. In the present work, we study the same model with disorder. Here disorder implies that negative interactions may occur with a probability $p$. In absence of extreme switches, the known critical point is at $p_c =1/4$ in the mean field model. With a nonzero value of $q$ that denotes the probability of such switches, the critical point is found to occur at $ p = \frac{1-q}{4}$ where the order parameter vanishes with a universal value of the exponent $β=1/2$. Stability analysis of initially ordered states near the phase boundary reveals the exponential growth/decay of the order parameter in the ordered/disordered phase with a timescale diverging with exponent $1$. The fully ordered state also relaxes exponentially to its equilibrium value with a similar behaviour of the associated timescale. Exactly at the critical points, the order parameter shows a power law decay with time with exponent $1/2$. Although the critical behaviour remains mean field like, the system behaves more like a two state model as $q \to 1$. At $q=1$ the model behaves like a binary voter model with random flipping occurring with probability $p$.
