谢林分凝模型的状态方程
A state equation for the Schelling's segregation model
摘要：
著名的谢林隔离模型最近被提出了一个无空间的版本，称为两个房间的模型，仍然是一个基于代理的格式，如原来的谢林模型。在本研究中，我们提出了一个新的，状态方程版本的谢林模型。新的方程是基于两个房间的模型，并推导出一组离散的地图。新方程的不动点解的解析和确认数值。特别是，我们发现，非常简单的状态方程可以合理地揭示谢林动力学的本质：集成，分离和倾斜。除了不动点解，周期解的确定和条件的极限环推导出解析。
英文摘要：
An aspatial version for the famous Schelling's segregation model has recently been proposed, which, called two-room model, is still in an agent-based format like the original Schelling model. In the present study, we propose a new, state equation version of the Schelling model. The new equation is based on the two-room model and is derived in terms of a set of discrete maps. Fixed point solutions for the new equation are found analytically and confirmed numerically. Especially, we show that the extremely simple state equations can reasonably reveal the essence of the Schelling dynamics: integration, segregation and tipping. In addition to the fixed point solutions, periodic solutions are identified and conditions of the limit cycles are derived analytically.
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