利用matlab和阻滞增长模型分析我国的人口变化规律。人口数量如下表单位：千万 年份 1954 1955 1956 1957 1958 1959 1960 1961 1962人口 602 615 628 646 660 6549 667 6603 6658年份 1963 1964 1965 1966 1967 1968 1969 1970 1971人口 6823 6984 7152 7354 75

% 定义年份和人口数量 year = [1954:1:2019]; pop = [60.2,61.5,62.8,64.6,66.0,65.49,66.7,66.03,66.58,68.23,69.84,71.52,73.54,75.46,77.45,79.60,81.83,84.11,86.20,88.19,90.04,91.64,93.07,94.35,95.61,96.90,98.12,99.39,100.86,102.33,103.68,105.10,106.68,108.40,110.16,111.87,113.52,115.08,116.49,117.84,119.18,120.49,121.76,123.01,124.19,125.27,126.26,127.19,128.04,128.84,129.61,130.37,131.10,130.79,132.47,133.13,133.77,134.41,135.07,135.74,136.43,137.12,137.87,138.64,139.27,139.77];

% 定义阻滞增长模型公式 f = @(p,x)(p(1)x.(1-p(2)*x/p(1)));

% 初始参数值 p0 = [150, 0.1];

% 进行拟合 [p,resnorm,~,exitflag,output] = lsqcurvefit(f,p0,year(1:end-1),pop(1:end-1));

% 输出拟合结果 r = p(1); x_m = p(2); disp(['r=',num2str(r)]); disp(['x_m=',num2str(x_m)]);

% 绘制原始数据和拟合函数图像 figure; plot(year, pop, 'bo', 'MarkerSize', 5); hold on; plot(year, f(p, year), 'r-', 'LineWidth', 1); xlabel('年份'); ylabel('人口数量(千万)'); legend('原始数据', '拟合函数'); title(['拟合结果 r=',num2str(r),', x_m=',num2str(x_m)]);

% 检验拟合结果 year_test = 2019; pop_test = f(p, year_test); disp(['2019年预测人口数量为',num2str(pop_test),'(实际值为139.77)'])