PROGRESS IN GEOGRAPHY ›› 2015, Vol. 34 ›› Issue (3): 321-329.doi: 10.11820/dlkxjz.2015.03.007
• Theoretical Model and GIS Application • Previous Articles Next Articles
Yanguang CHEN
Received:
2014-10-01
Revised:
2015-02-01
Online:
2015-03-25
Published:
2015-03-25
Yanguang CHEN. Simplicity, complexity, and mathematical modeling of geographical distributions[J].PROGRESS IN GEOGRAPHY, 2015, 34(3): 321-329.
Tab.1
Comparison between simple distributions and complex distributions"
视角 | 简单分布(有尺度分布) | 复杂分布(无尺度分布) |
---|---|---|
代表性函数 | 正态分布、泊松分布、指数分布 | 幂律分布、Gamma分布(某些情况) |
基本性质 | 有特征尺度(有效的平均值) | 无特征尺度(平均值无效) |
概率结构 | 有明确的概率结构 | 无确定的概率结构 |
数学判据 | 特征长度 | 标度指数 |
概率密度曲线 | 通常为趋中型:中间高、两端低 | 极端型:一端高、一端低 |
理论根据 | 大数定律和中心极限定理 | 分形几何学和标度理论 |
分析难度 | 难度低(尺度分析) | 难度高(标度分析) |
地理案例 | 城市人口密度分布 | 城市位序-规模分布 |
Tab.2
Comparison between simple systems and complex systems"
视角 | 简单系统 | 复杂系统 |
---|---|---|
分布性质 | 有特征尺度(平均值有效) | 无特征尺度(平均值无效) |
空间格局 | 规则几何学(微积分原理有效) | 不规则几何学(微积分原理常常失效) |
过程和关系 | 线性过程和关系(线性叠加原理有效) | 非线性过程和关系(线性叠加原理常常失效) |
概率分布 | 中庸分布(大数定律和中心极限定理有效) | 极端分布(大数定律和中心极限定理无效) |
分析方法 | 还原论有效(标准方法论) | 还原论无效(需要整体论) |
系统规律 | 时空平移对称(守恒原理有效) | 时空平移不对称(经典守恒原理无效) |
Tab.3
Comparison between exponential distributions and power-law distributions"
视角 | 指数分布(负指数分布) | 幂律分布(幂指数分布) |
---|---|---|
函数 | y=y0exp(-bx)=y0exp(-x/x0) | y=y1x-q |
曲线形态 | 极端型 | 极端型 |
自相关函数 | 拖尾(尾巴很肥) | 拖尾 |
偏自相关函数 | 一阶截尾(1次滞后处截断) | 拖尾(尾巴较瘦) |
时间效应 | 后效弱(时间记忆短) | 后效强(时间记忆长) |
空间效应 | 局域性(空间相关弱) | 长程作用(空间相关强) |
不变性 | 平移不变,微分不变 | 伸缩不变 |
对称性 | 尺度平移对称 | 尺度伸缩对称(标度对称) |
适用对象 | 简单系统 | 复杂系统 |
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