基于城市中心划分视角的人口–土地异速生长与经济发展研究：以广西壮族自治区为例
Research on Population-Land Allometric Growth and Economic Development from the Perspective of Urban Centralization: A Case Study of Guangxi Zhuang Autonomous Region
摘要: 随着全球城市化进程的加快，城市的发展已经成为一个多维复杂的议题。本研究以广西壮族自治区为例，基于城市中心划分视角，探讨了人口–土地异速生长与经济发展之间的联系。通过引入分形几何理论，量化城市形态的复杂性，并结合异速生长概念，分析了城市不同领域发展过程中的不均匀性。研究采用盒维数法和多径向分析法计算局部分形维数，并利用熵权法构建经济集聚指数，以评估城市经济的集聚效应。研究发现，桂林市在2014~2022年之间的局部分形维数在0~1.7之间，将其划分为四个阶段，反映城市化的不同进度。通过构建经济集聚指数与局部分形维数的模型，得出它们之间存在强烈的正相关性，表明城市结构的优化能够促进经济活动的集中程度。此外，广西各市的异速生长指数揭示了人口增长与土地扩张之间的非均匀性，对城市政策制定和规划具有重要意义。本研究为优化城市规划和实现区域协调发展提供了有价值的参考，能够更好地了解城市经济活动的分布特点，以及如何通过优化城市结构促进经济的均衡发展。
Abstract: With the acceleration of global urbanization, urban development has become a multi-dimensional and complex issue. This study, taking Guangxi Zhuang Autonomous Region as an example, explores the connection between population-land allometric growth and economic development from the perspective of urban centralization. By introducing fractal geometry theory, we quantify the complexity of urban morphology and analyze the unevenness in various development sectors of the city through the concept of allometric growth. The study employs box-counting dimension methods and multi-radial analysis to calculate local fractal dimensions, and utilizes the entropy weight method to construct an economic agglomeration index to assess the agglomeration effects of urban economies. The research finds that the local fractal dimension of Guilin City ranges between 0 and 1.7 from 2014 to 2022, dividing it into four stages that reflect different levels of urbanization. By constructing a model of the economic agglomeration index and local fractal dimension, a strong positive correlation between the two is revealed, indicating that the optimization of urban structure can promote the concentration of economic activities. Moreover, the allometric growth indices of various cities in Guangxi unveil the unevenness between population growth and land expansion, which holds significant implications for urban policy making and planning. This study provides valuable references for optimizing urban planning and achieving coordinated regional development, contributing to a better understanding of the distribution characteristics of urban economic activities and how optimizing urban structures can promote balanced economic growth.
文章引用：隋丽丽, 牛方萍. 基于城市中心划分视角的人口–土地异速生长与经济发展研究：以广西壮族自治区为例[J]. 应用数学进展, 2025, 14(1): 159-172. https://doi.org/10.12677/aam.2025.141019

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