表达式已经给出，求图像？

clc;close;clear;
x=0:0.1:200;
D=0.25;
Q=0.50;
lambda=0.1;% 0<lambad<1;
alpha=0.3;%-1<alpha<1;
beta=-0.1;
tau=0.1;%0<tau<1
f= @(x)((beta+tau*beta^2)*x.^2/4*D)-(beta+tau*beta^2)*(lambda*sqrt(D*Q)+2*D)*x/D^2;
C=(2*D*(alpha+tau*alpha*beta)-(beta+tau*beta^2)*(Q-4*Q*(lambda^2)-4*lambda*sqrt(D*Q)-3))/4*D^2;
E=-(2*D*lambda*(alpha+tau*alpha*beta)+(beta+tau*beta^2)*(lambda*Q*sqrt(D*Q)*(4*(lambda^2)-3)+D*Q*(8*(lambda^2)-4)+3*lambda*D*sqrt(D*Q)))/2*D^2;
a=@(x)D*x.^2+2*lambda*x*sqrt(D*Q)+Q;
b=E/(((1-lambda^2)*D*Q)^0.5);
m=@(x)(D*x+lambda*sqrt(D*Q))/(((1-lambda^2)*D*Q)^0.5);
P=@(x)exp((f(x)+b.*atan(m(x)))).*a(x).^C;
M = integral(P,0,inf);
N=1/M;
Pst=N*P(x);

表达式已经给出，要求画如下图像。

img

你好，三个图像代码：

clc;close;clear;
x=0:0.1:200;
D=0.25;
Q=0.50;
lambda=0.1;% 0<lambad<1;
alpha=0.3;%-1<alpha<1;
beta=-0.1;
tau=0.1;%0<tau<1
tau_arr = 0:0.01:1;
x_arr = zeros(size(tau_arr));
for i = 1:1:numel(tau_arr)
    tau = tau_arr(i);
f= @(x)((beta+tau*beta^2)*x.^2/4*D)-(beta+tau*beta^2)*(lambda*sqrt(D*Q)+2*D)*x/D^2;
C=(2*D*(alpha+tau*alpha*beta)-(beta+tau*beta^2)*(Q-4*Q*(lambda^2)-4*lambda*sqrt(D*Q)-3))/4*D^2;
E=-(2*D*lambda*(alpha+tau*alpha*beta)+(beta+tau*beta^2)*(lambda*Q*sqrt(D*Q)*(4*(lambda^2)-3)+D*Q*(8*(lambda^2)-4)+3*lambda*D*sqrt(D*Q)))/2*D^2;
a=@(x)D*x.^2+2*lambda*x*sqrt(D*Q)+Q;
b=E/(((1-lambda^2)*D*Q)^0.5);
m=@(x)(D*x+lambda*sqrt(D*Q))/(((1-lambda^2)*D*Q)^0.5);
P=@(x)exp((f(x)+b.*atan(m(x)))).*a(x).^C;
M = integral(P,0,inf);
N=1/M;
Pst=@(x)N*P(x);
QQ = @(x)Pst(x).*x;
RR = @(x)Pst(x).*x.*x;
SS = @(x)Pst(x).*x.*x.*x;
x_arr(i) = integral(QQ, 0, inf);
end
plot(tau_arr, x_arr)
xlabel('\tau'); ylabel('<x>')

img


clc;close;clear;
x=0:0.1:200;
D=0.25;
Q=0.50;
lambda_arr=0:0.01:0.99;% 0<lambad<1;
alpha=0.3;%-1<alpha<1;
beta=-0.1;
tau=0.1;%0<tau<1

sigma2_arr = zeros(size(lambda_arr));
for i = 1:1:numel(lambda_arr)
    lambda = lambda_arr(i);
f= @(x)((beta+tau*beta^2)*x.^2/4*D)-(beta+tau*beta^2)*(lambda*sqrt(D*Q)+2*D)*x/D^2;
C=(2*D*(alpha+tau*alpha*beta)-(beta+tau*beta^2)*(Q-4*Q*(lambda^2)-4*lambda*sqrt(D*Q)-3))/4*D^2;
E=-(2*D*lambda*(alpha+tau*alpha*beta)+(beta+tau*beta^2)*(lambda*Q*sqrt(D*Q)*(4*(lambda^2)-3)+D*Q*(8*(lambda^2)-4)+3*lambda*D*sqrt(D*Q)))/2*D^2;
a=@(x)D*x.^2+2*lambda*x*sqrt(D*Q)+Q;
b=E/(((1-lambda^2)*D*Q)^0.5);
m=@(x)(D*x+lambda*sqrt(D*Q))/(((1-lambda^2)*D*Q)^0.5);
P=@(x)exp((f(x)+b.*atan(m(x)))).*a(x).^C;
M = integral(P,0,inf);
N=1/M;
Pst=@(x)N*P(x);
QQ = @(x)Pst(x).*x;
RR = @(x)Pst(x).*x.*x;
SS = @(x)Pst(x).*x.*x.*x;
sigma2_arr(i) = integral(RR, 0, inf)/integral(QQ, 0, inf)^2-1;
end
plot(lambda_arr, sigma2_arr)
xlabel('\lambda'); ylabel('<\sigma^2>')

img

clc;close;clear;
x=0:0.1:200;
D=0.25;
Q=0.50;
alpha_arr=0:0.01:0.99;% 0<lambad<1;
alpha=0.3;%-1<alpha<1;
beta=-0.1;
tau=0.1;%0<tau<1
lambda=0.1;
sigma3_arr = zeros(size(alpha_arr));
for i = 1:1:numel(alpha_arr)
   alpha = alpha_arr(i);
f= @(x)((beta+tau*beta^2)*x.^2/4*D)-(beta+tau*beta^2)*(lambda*sqrt(D*Q)+2*D)*x/D^2;
C=(2*D*(alpha+tau*alpha*beta)-(beta+tau*beta^2)*(Q-4*Q*(lambda^2)-4*lambda*sqrt(D*Q)-3))/4*D^2;
E=-(2*D*lambda*(alpha+tau*alpha*beta)+(beta+tau*beta^2)*(lambda*Q*sqrt(D*Q)*(4*(lambda^2)-3)+D*Q*(8*(lambda^2)-4)+3*lambda*D*sqrt(D*Q)))/2*D^2;
a=@(x)D*x.^2+2*lambda*x*sqrt(D*Q)+Q;
b=E/(((1-lambda^2)*D*Q)^0.5);
m=@(x)(D*x+lambda*sqrt(D*Q))/(((1-lambda^2)*D*Q)^0.5);
P=@(x)exp((f(x)+b.*atan(m(x)))).*a(x).^C;
M = integral(P,0,inf);
N=1/M;
Pst=@(x)N*P(x);
QQ = @(x)Pst(x).*x;
RR = @(x)Pst(x).*x.*x;
SS = @(x)Pst(x).*x.*x.*x;
sigma2 = integral(RR, 0, inf)/integral(QQ, 0, inf)^2-1;
sigma3_arr(i) = integral(SS, 0, inf)/integral(QQ, 0, inf)^3 - 3*sigma2-1;
end
plot(alpha_arr, sigma3_arr)
xlabel('\alpha'); ylabel('<\sigma^3>')

img

。。。
plot(x,Pst);
grid on;

img