意见形成模型中的Van Kampen扩展方法
Van Kampen's expansion approach in an opinion formation model
摘要：
我们分析了一个简单的意见形成模型，包括两个政党，A和B，和一组I，未定的代理。我们假设A方和B方的支持者之间不相互作用，而只是通过群体I相互作用，并且存在非零的自发意见改变概率（A->I，B->I）。从主方程出发，通过van Kampen的Ω展开方法，我们得到了“宏观”演化方程，以及控制确定性行为周围波动的Fokker-Planck方程。在同样的方法中，我们也获得了关于小扰动的典型弛豫行为的信息。
英文摘要：
We analyze a simple opinion formation model consisting of two parties, A and B, and a group I, of undecided agents. We assume that the supporters of parties A and B do not interact among them, but only interact through the group I, and that there is a nonzero probability of a spontaneous change of opinion (A->I, B->I). From the master equation, and via van Kampen's Omega-expansion approach, we have obtained the "macroscopic" evolution equation, as well as the Fokker-Planck equation governing the fluctuations around the deterministic behavior. Within the same approach, we have also obtained information about the typical relaxation behavior of small perturbations.
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