昆山市人口指标的数学模型  

MATHEMATICAL MODELING OF POPULATION GROWTH IN KUNSHAN

作　　者：姚鑫[1,2,3] 杨桂山[1,3] 孙洪波[1,2,3] 万荣荣[1,3] 

机构地区：[1]中国科学院南京地理与湖泊研究所,江苏南京210008 [2]中国科学院研究生院,北京100039 [3]中国科学院南京地理与湖泊研究所湖泊与环境国家重点实验室,江苏南京210008

出　　处：《长江流域资源与环境》2010年第3期244-248,共5页Resources and Environment in the Yangtze Basin

基　　金：国家自然科学基金(40601098)

摘　　要：数学模型常用于人口指标变化趋势的拟合,以昆山市1985-2006年7种人口指标为研究对象,采用马尔萨斯模型、Logistic模型和Keyfitz模型进行模拟,结合历史资料分析人口指标变化背后的社会经济因素。研究结果表明：从整体拟合效果来看,Logistic模型表现良好,但这很大程度上在于其三参数优势,而不是人口增长面临最大人口上限的压力,即使某一时段反映出人口上限,该值也可能在下一时段被突破;由于人口指标增长转折点的存在,使利用数学模型进行人口预测的可信度降低,但利用转折点分段分析,了解其代表的政治、经济因素的影响,可以为未来的规划决策提供科学参考;昆山的发展历程明显分为3个阶段,而不是以往认为的5个阶段。Mathematical models are widely used to simulate the development trend of population.In this paper,four mathematical models,named as Malthusian model,Logistic model,linear regression model and Keyfitz model were studied on their capability of modeling the historical development trend of seven population variables of Kunshan,Jiangsu Province from 1985 to 2006.Results showed that,generally,Logistic model was better than other models according to determination coefficients.Then each index was analyzed separately with an aim to explain the differences between simulated and recorded numbers.From the results,it was concluded that：1） logistic model fitted well primarily because it had three parameters while other models had two,and the additional parameter Pm,which should stand for the upper limit of population increasing,did not have real sense in most cases;2） the prediction of future population by the use of mathematical modeling showed unfeasible for the existence of turning points in the development trend of population variables;3） combined with historical information of the research area,turning points could give a good description on the effects of political and economic factors occurred simultaneously;4） the development course of Kunshan should be divided into three stages,the developing stage,the adjustment stage and the overall developing stage,rather than five stages generally accepted previously.

关 键 词：人口指标 数学模型 转折点 

分 类 号：O141.4[理学—数学]