Statistical Regularities Of City-Size Distribution And Its Formation Mechanism

Cities, the gathering places of various socio-economic factors, are the space form and condition of the urban economy. Now refers to city-size distribution is generally thought of Zipf law, it is from another angle, reflecting the power-law exists between objective datas. The Zipf theory, reflects the relationship between city's ranks and sizes,has become important foundation of urban systems, and also become the focus of researchers' attentions in this field. In this paper, city-size distribution as the research object to study the formation mechanism of Zipf law.In this paper, we build models and analysis them. That part of the establishment of an agent-based evolutionary model of urban migration, it contains a number of sub-models. These sub-models have in common that they are used to simulate urban migration model, with the same operating environment, the biggest difference is that the migrate rules of the agent. Agent-based model essentially abandons the rational choice paradigm but emphasizes that the agents are limited rational. This model is based on the spatial distribution of the agent in the urban is not to study formation of a single city, through the interaction between the micro-agent to study the emergence of macro-economic phenomenon, is a bottom-up model. Through modeling and programming, attempt to use computer to simulation of the population migration behavior, using this method to study the urban population's rank-size distribution and its generation mechanism.The first model is a pure random walk model, city-size distribution subject to the same normal distribution. The second model added the migration rules, subject to choose the largest cities as their migration destination within vision,from the experiment,we find that the system reached steady state quickly and generate significant Zipf law. Draw the following conclusions through further validate,in the system,agent of the"differences"and the migration behavior of"preference dependent"characteristics are the two necessary conditions for urban migration model generated Zipf law."Differences"have more specific requires, in this article the distribution of agent's vision must be symmetrical. The third model adds a negative growth factor,-c·nj(t)2.Experimental results show that, as c increases, the size of the largest city decreases. And size of a growing number of cities will not grow.When the size makes the utility function biggest, the agents will not join or leave, this is not the fact, but also lead directly a number of the largest city in the running results, so wo should continue to optimize the model, and improve its immigrate rules, in the fourth model, by adding spillover diffusion effects and found that fit goodness greatly improve, the emergence of new cities become possible, and the agent's vision does not need to obey symmetric distribution, analyses the model algorithm, we get the conclusion that city-size distribution is Zipf law and to adjust the largest vision, you can get different Zipf index, which is also found the phenomenon of"data collapse",it reflects scale-free of the Zipf law distribution. In the fifth model adds the interaction between the agents, let the migrate rules close to the real migrate action of humans, found deflection occurred in small-scale. In general, the left of the distribution empirical data often performance non-power-law, so when the power-law behavior starts, that is very important. This article describes two simple methods to estimate minimum, BIC criteria and KS statistics; found that after remove the size below the minimum size, the sizedistribution show Zipf law.The final model adds growth mechanism to verify the necessity of the growth mechanism in the formation of the time dimension of the Zipf law, experimental results show that as the new agents access, the size of the largest city have increased, and however, the growth rate of cities number is less than the growth rate of the size of the largest city.In the last part of this article is empirical research, the size distribution of Zhejiang Province as the study object, the data selected in 1990 and 2000 census data to study the growth rate of the number of cities larger than the growth rate of the city size whether the citiy-size distribution is subject to Zipf law or not. City-size distribution of Zhejiang province obeys to Zipf law, and analysis characteristics of the city-size distribution carefully, thus facilitate the government to formulate effective policies and measures to let city develop in an appropriate scale, and the environment, coordinated economic development, in the path of sustainable development.