大学数学实验--实验四.pdf

凯里学院理学院数学与应用数学专业数学实验报告实验序号：日期：2009年 12月 12 日班级07 级数本（2）班姓名杨秀江学号2007406045 实验名称常微分方程数值解问题背景与实验目的：a.掌握用 MATLAB 软件求微分方程初值问题数值解的方法；b.通过实例学习用微分方程模型解决简化的实际问题；c.了解欧拉方法和龙格-库塔方法的基本思想和计算公式，及稳定性等概念。实验内容：两种群相互竞争模型如下：11122221(1)(1)dxxyr xsdtnndyyxr ysdtnn其中 x(t),y(t)分别为甲乙两种群的数量，1r，2r为它们的固有增长率，1n，2n为它们的最大容量。1s的含义是，对于供养甲的资源来说，单位数量的乙（相对2n）的消耗为单位数量甲（相对1n）消耗的1s倍，对2s可以作相应解释。该模型无解析解，试用数值方法研究以下问题：（1）设 r1=r2=1,n1=n2=100,s1=0.5,s2=2,初值 x0=y0=10,计算 x(t),y(t),画出它们的图形及图（x,y），说明时间 t 充分大了以后 x(t),y(t)的变化趋势（人们今天看到的已经是自然界长期演变的结局）。（2）改变 r1,r2,n1,n2,x0,y0,但 s1,s2不变（或保持 s11），计算并分析所得结果，若 s1=1.5(1),s2=0.7(0，即rxx/而捕食者的存在使食饵的增长率减小，设减小量与捕食者密度成正比，比例系数从而有ayrxx/。同样，捕食者离开了食饵无法生存，设它独自存在死亡率为常数d0,即dyy/，因为食饵的存在，从而使死亡率减少，设有减少量与食饵的密度成正比，有比例系数为b0，则)(/bxdyy。从而有当 bxd 时捕食者的密度增长。设有他们的初始值分别为x0，y0,从而有yyxxbxydyybxdyaxyrxxayrx00)0(,)0()()(模型求解：本题无解析解，故用龙格库塔方法求解此微分方程，程序如下：jz.m:function dx=jz(t,x,r1,r2,n1,n2,s1,s2)dx=r1*x(1)*(1-x(1)/n1-s1*x(2)/n2);r2*x(2)*(1-s2*x(1)/n1-x(2)/n2);%以 向 量形式表示微分方程jzdraw.m:h=0.1;%所取时间点间隔ts=0:h:30;%时间区间x0=10,10;%初始条件opt=odeset(reltol,1e-6,abstol,1e-9);%相对误差 1e-6，绝对误差 1e-9 t,x=ode45(jz,ts,x0,opt,1,1,100,100,0.5,2);%使用 5 级 4 阶龙格库塔公式计算t,x%输出 t,x(t),y(t)%后面的参数传给jz,分别是 r1,r2,n1,n2,s1,s2 plot(t,x,.-),grid%输出 x(t),y(t)的图形gtext(x(t),gtext(y(t),pause plot(x(:,1),x(:,2),.-),grid,%作 y(x)的图形gtext(x),gtext(y);文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 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ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10凯里学院理学院数学与应用数学专业实验过程记录（含：基本步骤、主要程序清单及异常情况记录等）利用 MATLAB 编程序计算常微分方程数值求解模型，源程序如下：function dx=jz(t,x,r1,r2,n1,n2,s1,s2)dx=r1*x(1)*(1-x(1)/n1-s1*x(2)/n2);r2*x(2)*(1-s2*x(1)/n1-x(2)/n2);h=0.1;ts=0:h:30;x0=10,10;opt=odeset(reltol,1e-6,abstol,1e-9);t,x=ode45(jz,ts,x0,opt,1,1,100,100,0.5,2);end t,x plot(t,x,.-),grid gtext(x(t),gtext(y(t),pause plot(x(:,1),x(:,2),.-),grid,gtext(x),gtext(y);用 MATLAB 计算：文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10凯里学院理学院数学与应用数学专业最后数值稳定在x=100,y=0 上，即物种甲达到最大值，物种乙灭绝。下面给出 x(t),y(t),和 x(y)的图形从第一张图可以看到，物种乙开始一段时间数量稍稍有所增长，10 年后就渐渐灭绝了，最后稳定状态就只剩下甲物种。实验结果报告：改变参数进一步讨论：下面在保持s1,s2不变的基础上，分别改变r1,r2；n1,n2；x0,y0 观察变化趋势：(1)改变 r1,r2:1.r1=r2=0.3 文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 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ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10凯里学院理学院数学与应用数学专业我们可以看到甲乙两物种最终结果仍然是甲达到数量极限而乙灭绝，但与原先不同的是变化速度减缓了，这是由于自然增长率r1,r2 变小的缘故（相当于变化率减小）。2.r1=5,r2=0.3 由于改变了自然增长率，我们可以看到甲物种更快地达到最大，乙物种灭绝减缓。3.r1=0.3,r2=5:文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10凯里学院理学院数学与应用数学专业由于一开始甲物种的数量相对较少（x/n1），所以乙物种得以快速增长，数量一度达到90 以上，但最终仍然灭绝。物种容量的改变并不能影响最终谁会灭绝。下面的情况证明了这一点：2n1=10，n2=10000：可见虽然 s1,s2都大于 1，但由于 s2更大，更严重消耗了乙物种的生存资源，使乙物种在竞争中灭绝。实验小结：文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10凯里学院理学院数学与应用数学专业思考与深入：假设微分方程有稳态解，则最终值满足：11122221(1)0(1)0dxxyr xsdtnndyyxr ysdtnn有四组解：00 xy，10 xny，20 xyn，111222121111sxns ssyns s第一种情况实际不可能发生，第二、三种情况上面有很多例子，对第四种情况，在此检验：1 s1=0.8,s2=0.7 时，11122212110.810045.4545110.80.7110.710068.1818110.80.7sxns ssyns s，与上面数值解完全相符。2 s1=s2=1.5 时，11122212111.510040111.51.5111.510040111.51.5sxns ssyns s，也与上面的数值解相符。教师评语：报告评分：指导教师签字：文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 ZO5U3O7C2B10文档编码:CZ5B2Y9U3R6 HH5H9F7O6Y6 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