Need to make surf plot in ode45

How to give command for making surf plot in ode45. I have coupled nonlinear ODE system. I need to run a surface diagram for variables using any 2 parameters. The following is the code for 2D plots. Please help me to run surf plot in MATLAB.

function ode
options = odeset('RelTol',1e-6,'Stats','on'); 
%initial conditions     
Xo = [0.5;0.7;2];  
tspan =linspace(0,100); 
tic 
[t,X] = ode45(@TestFunction,tspan,Xo,options); 
toc  
figure 
plot(t, X(:,1), 'red')
plot(t, X(:,2), 'blue')
plot(t, X(:,3), 'red')
return  
function [dx_dt]= TestFunction(~,x) 
r=0.05; k=0.1;  a=0.02; m=0.02; b=0.2; eta=0.06;
dx_dt(1)=r.*x(1).*(1-(x(1)./k))-a.*x(1).*x(3)+x(3).*eta;
dx_dt(2)=a.*x(1).*x(3)-m.*x(2)-b.*x(2)+h.*eta;
dx_dt(3)=b.*x(2)-eta.*x(3)-r.*x(1);
dx_dt = dx_dt';   
return 

Answer 1

[Chris]

options = odeset('RelTol',1e-6,'Stats','on'); 
%initial conditions     
Xo = [0.5;0.7;2];  

% Choose parameters t and a?
tspan =linspace(0,100);
a_vec = 0.01:0.005:0.03; 
for idx = 1:numel(a_vec)
    % Collect all X values into a 3D matrix. Additional parameters to
    % TestFunction can be added after ode45 options
    [t,X(:,:,idx)] = ode45(@TestFunction,tspan,Xo,options,a_vec(idx)); 
end

34 successful steps
0 failed attempts
205 function evaluations
34 successful steps
0 failed attempts
205 function evaluations
34 successful steps
0 failed attempts
205 function evaluations
34 successful steps
0 failed attempts
205 function evaluations
34 successful steps
0 failed attempts
205 function evaluations

figure 
plot(t, X(:,1), 'red')
hold on % keeps all three plots on the axes
plot(t, X(:,2), 'blue')
plot(t, X(:,3), 'red')

figure
tiledlayout(1,3)
nexttile
% Make a surface for each X0
surf(a_vec,t,squeeze(X(:,1,:))) 
% Squeeze removes dimensions of size 1, turning this slice into a 2d matrix
nexttile
surf(a_vec,t,squeeze(X(:,2,:)))
nexttile
surf(a_vec,t,squeeze(X(:,3,:))) 

function [dx_dt]= TestFunction(~,x,a) 
    r=0.05; k=0.1;  %a=0.02; 
    m=0.02; b=0.2; eta=0.06; h=1;
    dx_dt(1)=r.*x(1).*(1-(x(1)./k))-a.*x(1).*x(3)+x(3).*eta;
    dx_dt(2)=a.*x(1).*x(3)-m.*x(2)-b.*x(2)+h.*eta;
    dx_dt(3)=b.*x(2)-eta.*x(3)-r.*x(1);
    dx_dt = dx_dt';   
end 

[Suganya G]

Thank you!! This is the exact one which I need. But if I run this, the error is displayed like

Undefined function 'tiledlayout' for input arguments of type 'double'.

Error in surfcode (line 21)

tiledlayout(1,3)

[Walter Roberson]

https://www.mathworks.com/help/matlab/ref/tiledlayout.html

tiledlayout is R2019b or later. You did not specify which MATLAB release you are using, so we are permitted to assume that you are more up to date than that.

You can make calls to subplot() to arrange plots.

[Suganya G]

It is working. Thanks a lot!!

Answer 2

[Walter Roberson]

ode

37 successful steps
0 failed attempts
223 function evaluations
Elapsed time is 0.086187 seconds.

function ode
    options = odeset('RelTol',1e-6,'Stats','on'); 
    %initial conditions     
    Xo = [0.5;0.7;2];  
    tspan =linspace(0,100); 
    tic 
    [t,X] = ode45(@TestFunction,tspan,Xo,options); 
    toc  
    figure 
    F = scatteredInterpolant(t, X(:,1), X(:,2));
    minx1 = min(X(:,1)); maxx1 = max(X(:,1));
    xvec = linspace(minx1, maxx1, 100);
    [T, X] = meshgrid(t, xvec);
    X2 = F(T, X);
    surf(T, X, X2);
    xlabel('t'); ylabel('x(:,1)'); zlabel('x(:,2)');
end

function [dx_dt]= TestFunction(~,x) 
    r=0.05; k=0.1;  a=0.02; m=0.02; b=0.2; eta=0.06;
    h = .1;  %need SOME value
    dx_dt(1)=r.*x(1).*(1-(x(1)./k))-a.*x(1).*x(3)+x(3).*eta;
    dx_dt(2)=a.*x(1).*x(3)-m.*x(2)-b.*x(2)+h.*eta;
    dx_dt(3)=b.*x(2)-eta.*x(3)-r.*x(1);
    dx_dt = dx_dt';   
end 

[Suganya G]

Thanks for the relpy. Since I need x and y axis as parameters, I tried to change x(:,1) in terms of parameter a in this part

F = scatteredInterpolant(t, a_vec, X(:,2));

mina = 0.001; maxa = 0.003;

a_vec = linspace(mina, maxa, 100);

[T, X] = meshgrid(t, a_vec);

X2 = F(T, X);

surf(T, X, X2);

It didn't work. But I will use your code for in future work. Thanks!!