A dynamic phase transition model for spatial agglomeration processes.
A dynamic phase transition model for spatial agglomeration processes.
复制标题
空间聚集过程的动态相变模型。
DOI：
10.1111/j.1467-9787.1987.tb01181.x
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发表时间：
1987
影响因子：
3
通讯作者：
G. Haag
中科院分区：
文献类型：
--
作者：
W. Weidlich;G. Haag
提出了人口迁移的非线性模型，以便为大都市区的形成提供动态解释。 “在第 2 节中，根据区域人口数量平均值的速率方程介绍了模型，并特别选择了个体转移率。第 3 节给出了概念和结果的概述，以方便对数学推导细节不感兴趣的读者。第 4 节推导出速率方程的平稳解，即系统的平衡。第 5 节处理模型方程的时间相关解，重点是精确解析 沿着所谓的对称路径的解。第 6 节分析对称路径解的动态稳定性，并确定哪些稳态是不稳定的，哪些是稳定的平衡态。”
A nonlinear model of population migration is presented in order to provide a dynamic explanation for the formation of metropolitan areas. "In Section 2 the model is introduced in terms of the rate equations for the mean values of the regional population numbers with specifically chosen individual transition rates. Section 3 gives a survey of concepts and results for the convenience of the reader not interested in the details of the mathematical derivations. Section 4 derives the stationary solutions of the rate equations, that is, the equilibria of the system. Section 5 treats the time dependent solutions of the model equations focussing on the exact analytic solutions along so-called symmetry paths. Section 6 analyzes the dynamic stability of the symmetry path solutions and decides which stationary states are unstable and which are stable equilibrium states."