Scaling Law between Urban Electrical Consumption and Population in China

The relation between the household electrical consumption

Y

and population

N

for Chinese cities in 2006 has been investigated with the power law scaling form

$Y = A_0 N^{\beta}$

. It is found that the Chinese cities should be divided into three categories characterized by different scaling exponent

β

. The first category, which includes the biggest and coastal cities of China, has the scaling exponent

β

> 1. The second category, which includes mostly the cities in central China, has the scaling exponent

β

 ≈ 1. The third category, which consists of the cities in northwestern China, has the scaling exponent

β

< 1 . Using a urban growth equation, different ways of city population evolution can be obtained for different

β

. For

β

< 1 , population evolutes always to a fixed point population

N

f

from below or above depending on the initial population. For

β

> 1, there is also a fixed point population

N

f

. If the initial population

N

(0) > 

N

f

, the population increases very fast with time and diverges within a finite time. If the initial population

N

(0) < 

N

f

, the population decreases with time and collapse finally. The pattern of population evolution in a city is determined by its scaling exponent and initial population.