无组织偏析的动力系统模型
A dynamical systems model of unorganised segregation
摘要：
从现代动力系统理论的角度考虑了谢林的两种群无组织分离的有界邻域模型（BNM）。我们推导出一个谢林动力系统，并进行了一个完整的定量分析系统的情况下，在两个人口的线性公差表。在这样做，我们恢复和概括谢林的定性结果。对于无限人口流动的情况下，我们推导出了参数空间中稳定的综合人口混合区域的精确公式。我们展示了如何邻里小费可以充分解释的吸引力盆地。对于限制人口流动的情况下，我们得到了新的人口混合发生的确切标准，并确定稳定的情况下。我们将展示如何将我们的方法应用于非线性公差表，说明我们的方法与数值模拟。我们将谢林动力系统中的每个术语与社会意义联系起来。特别是，我们表明，在存在另一个种群的情况下，一个种群的动态可以总结如下{种群变化率} = {邻居的内在流行度} - {邻居的有限大小} - {其他种群的存在}通过从这个角度来处理动态，我们有一种与容忍度表互补的方法。
英文摘要：
We consider Schelling's bounded neighbourhood model (BNM) of unorganised segregation of two populations from the perspective of modern dynamical systems theory. We derive a Schelling dynamical system and carry out a complete quantitative analysis of the system for the case of a linear tolerance schedule in both populations. In doing so, we recover and generalise Schelling's qualitative results. For the case of unlimited population movement, we derive exact formulae for regions in parameter space where stable integrated population mixes can occur. We show how neighbourhood tipping can be adequately explained in terms of basins of attraction. For the case of limiting population movement, we derive exact criteria for the occurrence of new population mixes and identify the stable cases. We show how to apply our methodology to nonlinear tolerance schedules, illustrating our approach with numerical simulations. We associate each term in our Schelling dynamical system with a social meaning. In particular we show that the dynamics of one population in the presence of another can be summarised as follows {rate of population change} = {intrinsic popularity of neighbourhood} - {finite size of neighbourhood} - {presence of other population} By approaching the dynamics from this perspective, we have a complementary approach to that of the tolerance schedule.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
