2007国内数学建模竞赛上交试卷新

1、口增长的一、 摘要引入了自动控制原理中的信号流图反映各变量之间的关系，以目前计划规定理论总和率作为输入来分析人口模型各个控制量间的影响，进而建立以时间和为变量的偏微分方程。对于城、乡、镇分别考虑城出生率函数、率函数、人口率函数等，通过数据拟合求解出生率函数、率函数、及人口率函数。代入偏微分方程，利用 Mathematica求解偏微分方程组的解，这里可根据城乡镇的实际拟合函数设定不同的参数值，对模型进行精确化处理。近而对未来口进行，中国中短期和长期的也分参数个性不同分别。：信号流图；人口总和率二、问题重述试从中国的实际情况和人口增长的上述特点（化进程、出生人口性别比持续升高，以及乡村人口城镇化等

2、）出发，参考相关数据，建立口增长的数学模型，并由此人口增长的中短期和长期趋势做出；特别要模型中的优点与不足之处。三、符号系统1、在该最优解的控制下,使人口系统从初态影响出生率，即有：率=a=-1.7176555,b=0.072426636,c=6.690232e-40镇人口率函数乡:八模型的应用1、当总人口（2）出生率、率以及人口率本质上均为 t 和 x 的二元函数，在均不受两者影响的情况下可以作为常值来处理，如本文所示。但是当他们受自变量的影响很大时，则仍为变量。从而使方程更加复杂，甚至无解。参考文献：1等，系统建模，国防工业，20062霖等，符号运算及其应用，国防工业，20043等，数学模

3、型，：高等教育，20034，与科学计算，：电子工业，2003附表一2005 年城镇乡出生率城出生率镇出生率乡出生率150.01380.03840.176160.1850.33820.8835170.84531.86963.4086182.82445.26410.0492197.962314.414321.15842021.467434.797350.35532136.609260.128578.43682250.66173.775188.87322379.1198100.44103.64542478.124594.557188.07122576.250879.381678.06722678.5

4、5773.18666.85532769.80460.154657.22232855.58449.075248.08162948.445.189949.06843040.80640.316844.97353134.012838.756248.44043227.631833.523239.38553322.131227.219533.54623418.5522.588626.30743514.079817.453422.1676369.249413.387815.6492377.123211.028512.5557383.78845.63297.4298393.16784.0815.9267402

5、.6733.52983.6181411.77761.60592.3114421.50061.57081.976430.7831.13971.107440.33280.54990.7515450.51680.51330.517460.5490.24380.485470.3850.38080.4623480.43160.75660.6552490.56240.44020.592附表二2005 年城镇乡率城镇乡率率率09.414810.275219.097511.53640.79321.942120.62780.4951.422131.0120.5280.811140.8580.3910.79665

6、0.90730.62040.82360.70920.38520.694470.81030.52060.472680.7790.23050.650490.82640.35510.805100.7780.52110.8554110.83020.35530.8562120.87520.61710.8783130.78060.6580.6725141.1640.36670.9339151.29250.53041.2835161.13330.90311.5858171.2440.78081.4116181.65241.10151.8224191.41190.86991.622201.20710.5224

7、1.4469211.31670.83831.2631221.48450.96271.5062231.51120.76541.411241.55680.78721.3702251.32820.63221.6836261.49440.94641.4155271.651524.5641.5123281.55761.19271.5511291.82681.81662.0705301.72641.28592.031311.91741.31222.5538322.291.87712.8439332.43321.66832.9142342.72642.04153.2828352.73152.82963.60

8、54362.8982.51883.5816373.0523.1464.1731382.70882.20183.7053393.16642.724.2737403.61553.55584.5301413.24924.17273.9742424.75363.72615.0106434.02943.81934.4472443.07921.67232.721453.68832.5443.6998464.31012.92343.445474.39324.36745.0475486.05854.63416.7086495.554.08246.082506.2246.32587.0745515.74996.

9、01287.0963525.90215.61297.9066537.16326.35257.915547.40556.34728.398557.0086.97118.2875566.92846.98889.3407577.62266.03527.9888587.9986.36639.5605599.5326.68949.48616010.04967.27110.6836619.84327.69649.57226211.35887.789310.31046312.63047.507211.17846411.91458.290312.90126515.45169.162914.3526613.64

10、67.905611.86956718.002910.812714.95616820.378412.30315.87446922.655212.871718.26347024.08514.105520.99477124.081912.647617.56737228.364414.787223.6857331.479414.923321.44247430.233112.710220.3937536.528616.525423.92777640.035213.487120.04187743.595216.132921.36827848.882713.8622.38397949.310214.874820.37218057.32716.458322.56528160.36612.687820.00648263.800112.680318.46168371.672412.305518.3