2007國內數學建模競賽上交試卷新

1、口增長的一、 摘要引入了自動控制原理中的信號流圖反映各變量之間的關系，以目前計劃規(guī)定理論總和率作為輸入來分析人口模型各個控制量間的影響，進而建立以時間和為變量的偏微分方程。對于城、鄉(xiāng)、鎮(zhèn)分別考慮城出生率函數、率函數、人口率函數等，通過數據擬合求解出生率函數、率函數、及人口率函數。代入偏微分方程，利用 Mathematica求解偏微分方程組的解，這里可根據城鄉(xiāng)鎮(zhèn)的實際擬合函數設定不同的參數值，對模型進行精確化處理。近而對未來口進行，中國中短期和長期的也分參數個性不同分別。：信號流圖；人口總和率二、問題重述試從中國的實際情況和人口增長的上述特點（化進程、出生人口性別比持續(xù)升高，以及鄉(xiāng)村人口城鎮(zhèn)化等

2、）出發(fā)，參考相關數據，建立口增長的數學模型，并由此人口增長的中短期和長期趨勢做出；特別要模型中的優(yōu)點與不足之處。三、符號系統(tǒng)1、在該最優(yōu)解的控制下,使人口系統(tǒng)從初態(tài)影響出生率，即有：率=a=-1.7176555,b=0.072426636,c=6.690232e-40鎮(zhèn)人口率函數鄉(xiāng):八模型的應用1、當總人口（2）出生率、率以及人口率本質上均為 t 和 x 的二元函數，在均不受兩者影響的情況下可以作為常值來處理，如本文所示。但是當他們受自變量的影響很大時，則仍為變量。從而使方程更加復雜，甚至無解。參考文獻：1等，系統(tǒng)建模，國防工業(yè)，20062霖等，符號運算及其應用，國防工業(yè)，20043等，數學模

3、型，：高等教育，20034，與科學計算，：電子工業(yè)，2003附表一2005 年城鎮(zhèn)鄉(xiāng)出生率城出生率鎮(zhèn)出生率鄉(xiāng)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 年城鎮(zhèn)鄉(xiāng)率城鎮(zhèn)鄉(xiāng)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