论文标题
具有随机极端开关的三个国家意见形成模型中的非平衡动力学
Non-equilibrium dynamics in a three state opinion formation model with stochastic extreme switches
论文作者
论文摘要
我们研究了三个状态动力学交换模型的舆论形成模型的非平衡动力学，其中可能在极端状态之间进行切换，具体取决于参数$ q $的值。对于任何$ Q $，得出并分析了平均场动力学方程。系统在\ cite {bcs}中使用的进化规则下的命运表明，它取决于$ q $的值和一般的初始状态。对于$ q = 1 $，可以最大程度地允许极端交换机，在动态中获得了准保存，这使其与选民模型相等。对于一般$ Q $值，获得了“冷冻”无序的固定点，可作为所有最初无序状态的吸引子。对于其他初始状态，订单参数随时间$ t $作为$ \ exp [α（q）t] $生长，其中$α= \ frac {1-q} {1-q} {3-q} $ for $ q \ neq 1 $，并遵循$ q = 1 $ $ q = 1 $的功率法律行为。使用基于完全连接的代理模型的数值仿真提供了其他结果，例如退出概率的系统大小依赖性和共识时间，进一步加剧了模型的不同行为，以$ q = 1 $和$ q \ neq 1 $。将结果与其他知名动力学系统中的非平衡现象进行了比较。
We investigate the non-equilibrium dynamics of a three state kinetic exchange model of opinion formation, where switches between extreme states are possible, depending on the value of a parameter $q$. The mean field dynamical equations are derived and analysed for any $q$. The fate of the system under the evolutionary rules used in \cite{BCS} shows that it is dependent on the value of $q$ and the initial state in general. For $q=1$, which allows the extreme switches maximally, a quasi-conservation in the dynamics is obtained which renders it equivalent to the voter model. For general $q$ values, a "frozen" disordered fixed point is obtained which acts as an attractor for all initially disordered states. For other initial states, the order parameter grows with time $t$ as $\exp[α(q) t]$ where $α= \frac{1-q}{3-q}$ for $q\neq 1$ and follows a power law behaviour for $q=1$. Numerical simulations using a fully connected agent based model provide additional results like the system size dependence of the exit probability and consensus times that further accentuate the different behaviour of the model for $q=1$ and $q\neq 1$. The results are compared with the non-equilibrium phenomena in other well known dynamical systems.
