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 = A0N β . 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 Nf from below or above depending on the initial population. For β > 1, there is also a fixed point population Nf . If the initial population N(0) > Nf , the population increases very fast with time and diverges within a finite time. If the initial population N(0) < Nf , 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.