1實(shí)驗(yàn)81捕魚業(yè)的持續(xù)收獲-產(chǎn)量模型實(shí)驗(yàn)72種群的相互競(jìng)爭(zhēng)

1、1實(shí)驗(yàn)8-1打魚業(yè)的連續(xù)收獲產(chǎn)量模型實(shí)驗(yàn)7-2種群的互相競(jìng)爭(zhēng)(1)1實(shí)驗(yàn)8-1打魚業(yè)的連續(xù)收獲產(chǎn)量模型實(shí)驗(yàn)7-2種群的互相競(jìng)爭(zhēng)(1)14/141實(shí)驗(yàn)8-1打魚業(yè)的連續(xù)收獲產(chǎn)量模型實(shí)驗(yàn)7-2種群的互相競(jìng)爭(zhēng)(1)河北大學(xué)數(shù)學(xué)模型實(shí)驗(yàn)實(shí)驗(yàn)報(bào)告班級(jí)專業(yè)15計(jì)科2班姓名張宇軒學(xué)號(hào)20151101006實(shí)驗(yàn)地址C1-229指導(dǎo)老師司建輝成績(jī)實(shí)驗(yàn)項(xiàng)目1.實(shí)驗(yàn)8-1打魚業(yè)的連續(xù)收獲產(chǎn)量模型2.實(shí)驗(yàn)7-2種群的互相競(jìng)爭(zhēng)（1）3.實(shí)驗(yàn)7-3種群的互相競(jìng)爭(zhēng)（2）一、實(shí)驗(yàn)?zāi)康膶W(xué)會(huì)利用MATLAB進(jìn)行實(shí)驗(yàn)，學(xué)會(huì)使用符號(hào)表達(dá)式，嫻熟掌握用函數(shù)solve求解代數(shù)方程組，復(fù)習(xí)在MATLAB中繪圖方法，合理使用函數(shù)text、a

2、xis、grid等。二、實(shí)驗(yàn)要求實(shí)驗(yàn)8-1打魚業(yè)的連續(xù)收獲產(chǎn)量模型運(yùn)轉(zhuǎn)下邊的m文件，并把相應(yīng)結(jié)果填空，即填入“_”。clear;clc;%無捕撈條件下單位時(shí)間的增加量：f(x)=rx(1-x/N)%捕撈條件下單位時(shí)間的捕撈量：h(x)=Ex%F(x)=f(x)-h(x)=rx(1-x/N)-Ex%捕撈狀況下漁場(chǎng)魚量知足的方程：x(t)=F(x)%知足F(x)=0的點(diǎn)x為方程的均衡點(diǎn)%求方程的均衡點(diǎn)symsrxNE;%定義符號(hào)變量Fx=r*x*(1-x/N)-E*x;%創(chuàng)立符號(hào)表達(dá)式x=solve(Fx,x)%求解F(x)=0（求根）%獲取兩個(gè)均衡點(diǎn)，記為：%x0=_,x1=_x0=x(2);x

3、1=x(1);%符號(hào)變量x的構(gòu)造種類成為%求F(x)的微分F(x)symsx;%定義符號(hào)變量x的構(gòu)造種類為dF=diff(Fx,x);dF=simple(dF)%簡(jiǎn)化符號(hào)表達(dá)式%得F(x)=_%求F(x0)并簡(jiǎn)化dFx0=subs(dF,x,x0);%將x=x0代入符號(hào)表達(dá)式dFdFx0=simple(dFx0)%得F(x0)=_%求F(x1)dFx1=subs(dF,x,x1)%得F(x1)=_%若Er，有F(x0)0，故x0點(diǎn)穩(wěn)固，x1點(diǎn)不穩(wěn)固（依據(jù)均衡點(diǎn)穩(wěn)固性的準(zhǔn)則）；%若Er，則結(jié)果正好相反。%在漁場(chǎng)魚量穩(wěn)固在x0的前提下（Er），求E使連續(xù)產(chǎn)量h(x0)達(dá)到最大hm。%經(jīng)過剖析（賜教

4、材p216圖1），只要求x0*使f(x)達(dá)到最大，且hm=f(x0*)。symsrxNfx=r*x*(1-x/N);df=diff(fx,x);x0=solve(df,x)%得x0*=_hm=subs(fx,x,x0)%得hm=_%又由x0*=N(1-E/r)，可得E*=_%產(chǎn)量模型的結(jié)論是：%將捕撈率控制在固有增加率的一半（E=r/2）時(shí)，能夠獲取最大的連續(xù)產(chǎn)量。提示符號(hào)簡(jiǎn)化函數(shù)simple的格式：simple(S)對(duì)符號(hào)表達(dá)式S試試多種不一樣的算法簡(jiǎn)化，以顯示S表達(dá)式的長(zhǎng)度最短的簡(jiǎn)化形式。變量替代函數(shù)sub的格式：Subs(S,OLD,NEW)將符號(hào)表達(dá)式S中的OLD變量替代為NEW變量。

5、實(shí)驗(yàn)7-2種群的互相競(jìng)爭(zhēng)（1）增補(bǔ)以下指出的程序段，而后運(yùn)轉(zhuǎn)該m文件，比較教材上的相應(yīng)結(jié)果。clear;clc;%甲乙兩個(gè)種群知足的增加方程：x1(t)=f(x1,x2)=r1*x1*(1-x1/N1-k1*x2/N2)x2(t)=g(x1,x2)=r2*x2*(1-k2*x1/N1-x2/N2)%求方程的均衡點(diǎn)，即解代數(shù)方程組f(x1,x2)=0g(x1,x2)=0編寫出該程序段。提示（1）使用符號(hào)表達(dá)式；（2）用函數(shù)solve求解代數(shù)方程組；（3）調(diào)整解（均衡點(diǎn)）的次序放入P中（見下邊說明所示），P的構(gòu)造種類為，P的第1列對(duì)應(yīng)x1，第2列對(duì)應(yīng)x2。%得4個(gè)均衡點(diǎn)：%P(1)=P1（%P(2

6、)=P2（N1，0）0，N2）%P(3)=P3（N1*(-1+k1)/(-1+k2*k1)，N2*(-1+k2)/(-1+k2*k1)）%P(4)=P4（0，0）%均衡點(diǎn)位于第一象限才存心義，故要求P3：k1,k2同時(shí)小于1，或同時(shí)大于1。%判斷均衡點(diǎn)的穩(wěn)固性（參照教材p224）fx1=diff(f,x1);fx2=diff(f,x2);gx1=diff(g,x1);gx2=diff(g,x2);A=fx1,fx2;gx1,gx2symsx1x2;p=subs(-(fx1+gx2),x1,x2,P(:,1),P(:,2);p=simple(p);%簡(jiǎn)化符號(hào)表達(dá)式pq=subs(det(A),x

7、1,x2,P(:,1),P(:,2);q=simple(q);Ppq%獲取教材p225表1的前3列，經(jīng)測(cè)算可得該表的第4列，即穩(wěn)固條件。實(shí)驗(yàn)7-3種群的互相競(jìng)爭(zhēng)（2）求微分方程組的數(shù)值解，分別畫出教材p227中的圖2(a)、(b、(c)。相關(guān)數(shù)據(jù)參賜教材p227中“計(jì)算與考證”。提示（1）求微分方程組的數(shù)值解可參照教材p140的程序。（2）在figure(1)中繪圖2(a)，在figure(2)中繪圖2(b)，在figure(3)中繪圖2(c)。在程序中，figure(圖形編號(hào))用于定位對(duì)應(yīng)圖形。3）使用text(x,y,表記文本)，坐標(biāo)點(diǎn)(x,y)在“表記文本”的左側(cè)，調(diào)整(x,y)值，使“

8、表記文本”放在圖中的適合地點(diǎn)。（4）用axis(xminxmaxyminymax)控制坐標(biāo)的刻度范圍。（5）用gridon翻開網(wǎng)格，gridoff封閉網(wǎng)格。（6）用holdon把要畫的圖形保持在以前在同一figure上所畫的圖形中（同一坐標(biāo)系）。（7）圖2(c)中的兩“點(diǎn)線”直線，一條的兩個(gè)端點(diǎn)為(0,1)和(1,0)，另一條的兩個(gè)端點(diǎn)為(0,2)和(1.6,0)。三、實(shí)驗(yàn)內(nèi)容1實(shí)驗(yàn)8-1打魚業(yè)的連續(xù)收獲產(chǎn)量模型symsrxNE;Fx=r*x*(1-x/N)-E*x;x=solve(Fx,x)x0=x(2);x1=x(1);symsx;dF=diff(Fx,x);dF=simple(dF)dF

9、x0=subs(dF,x,x0);dFx0=simple(dFx0)dFx1=subs(dF,x,x1)symsrxNfx=r*x*(1-x/N);df=diff(fx,x);x0=solve(df,x)hm=subs(fx,x,x0)2實(shí)驗(yàn)7-2種群的互相競(jìng)爭(zhēng)（1）symsr1r2x1x2N1N2k1k2;F=r1*x1*(1-x1/N1-k1*x2/N2);G=r2*x2*(1-k2*x1/N1-x2/N2);x1,x2=solve(F,G)P=x1(2,4,1,3),x2(2,4,1,2);fx1=diff(F,x1);fx2=diff(F,x2);gx1=diff(G,x1);gx2=

10、diff(G,x2);A=fx1,fx2;gx1,gx2;symsx1x2;p=subs(-(fx1+gx2),x1,x2,P(:,1),P(:,2);p=simple(p);q=subs(det(A),x1,x2,P(:,1),P(:,2);q=simple(q);Ppq實(shí)驗(yàn)7-3種群的互相競(jìng)爭(zhēng)（2）M文件中：functiony=fun(t,x)r=1;d=0.5;a=0.1;b=0.02;y=(r-a*x(2).*x(1);(-d+b*x(1).*x(2);ts=0:0.1:15;x0=25,2;t,x=ode45(fun,ts,x0);t,xplot(t,x),grid,gtext(x(

11、t),gtext(y(t),pause,plot(x(:,1),x(:,2),gridt,x=ode45(fun,ts,x0);四、實(shí)驗(yàn)結(jié)果及其剖析1實(shí)驗(yàn)8-1打魚業(yè)的連續(xù)收獲產(chǎn)量模型x=0-N*(-r+E)/rdF=r-2*r*x/N-EdFx0=-r+EdFx1=r-Ex0=1/2*NE=r/2剖析：將捕撈率控制在固有增加率的一半（E=r/2）時(shí)，能夠獲取最大的連續(xù)產(chǎn)量。2實(shí)驗(yàn)7-2種群的互相競(jìng)爭(zhēng)（1）x1=0N10N1*(-1+k1)/(-1+k2*k1)x2=00N2N2*(-1+k2)/(-1+k2*k1)A=r1*(1-x1/N1-k1*x2/N2)-r1*x1/N1,-r1*x1

12、*k1/N2-r2*x2*k2/N1,r2*(1-k2*x1/N1-x2/N2)-r2*x2/N23實(shí)驗(yàn)7-3種群的互相競(jìng)爭(zhēng)（2）ans=025.00002.00000.100027.08182.00410.200029.33442.01700.300031.76892.03940.400034.39612.07260.500037.22582.11780.600040.26732.17670.700043.50122.25340.800046.93602.35030.900050.60722.46831.000054.53012.61061.100058.69992.78191.200063

13、.09172.98911.300067.66043.24111.400072.34093.54841.500077.04793.92381.600081.67594.38191.700086.09964.93911.800090.17325.61401.900093.73116.42682.000096.58737.40002.100098.53608.55772.200099.30559.92342.300098.614311.50852.400096.285113.30672.500092.247215.28822.600086.585317.39472.700079.534919.542

14、72.800071.536421.62252.900063.084823.53003.000054.623625.18193.100046.544126.51633.200039.186027.49213.300032.793228.09783.400027.336828.37663.500022.737528.37643.600018.913428.14263.700015.777127.71783.800013.235427.14263.900011.187326.45564.00009.527825.69114.10008.175824.87404.20007.068424.02454.

15、30006.159223.15804.40005.418522.28534.50004.812921.41624.60004.312420.55824.70003.896719.71644.80003.550018.89484.90003.260118.09615.00003.018117.32195.10002.815416.57355.20002.646015.85155.30002.504715.15625.40002.387214.48755.50002.289813.84545.60002.209913.22955.70002.145512.63935.80002.095312.07

16、405.90002.057811.53306.00002.031711.01546.10002.016210.52076.20002.010610.04796.30002.01439.59646.40002.02709.16536.50002.04838.75396.60002.07818.36146.70002.11647.98706.80002.16327.63006.90002.21887.28977.00002.28336.96547.10002.35736.65657.20002.44106.36227.30002.53516.08217.40002.64015.81557.5000

17、2.75665.56187.60002.88555.32047.70003.02765.09107.80003.18374.87297.90003.35494.66568.00003.54244.46888.10003.74784.28198.20003.97234.10468.30004.21743.93658.40004.48473.77738.50004.77613.62658.60005.09373.48388.70005.43983.34908.80005.81713.22178.90006.22833.10179.00006.67662.98889.10007.16532.8826

18、9.20007.69782.78319.30008.27812.69009.40008.91002.60329.50009.59802.52259.600010.34682.44799.700011.16202.37949.800012.04942.31669.900013.01532.259610.000014.06652.208410.100015.21022.162910.200016.45412.123310.300017.80632.089810.400019.27552.062710.500020.87082.042210.600022.60162.028710.700024.47

19、792.022810.800026.51022.024910.900028.70932.035511.000031.08442.055811.100033.64162.087511.200036.39822.130811.300039.36802.186911.400042.55982.257311.500045.97762.344711.600049.62052.452511.700053.48292.584911.800057.55392.746811.900061.81802.944112.000066.25493.183412.100070.84283.469212.200075.52223.812912.300080.19004.234812.400084.72134.754512.500088.96865.391812.600092.76226.165812.7000