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.

Error that appear when run the code:

Error in proj (line 20)

surf(a_vec,t,squeeze(X(:,1,:))) ;

Code below:

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
surf(a_vec,t,squeeze(X(:,1,:))) ;

% Squeeze removes dimensions of size 1, turning this slice into a 2d matrix

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 

Answer 1

[Karim]

Hi see below for some comments in the code on how to set the dimmensions to call the surf command.

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;

% ease the coding and readability
num_t = numel(tspan);
num_a = numel(a_vec);
num_x = numel(Xo);

% allocate output
X = zeros(num_t,num_x,num_a);

for idx = 1:num_a
    % 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

% make sure we have the proper dimmensions before calling surf
plot_t = repmat(t,1,num_a);
plot_a = repmat(a_vec,num_t,1);
plot_x = squeeze(X(:,1,:));

% create the surf plot
figure
surf(plot_t,plot_a,plot_x)
xlabel('t values')
ylabel('a values')
zlabel('x values')
grid on

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 

[T K]

@Karim Thank you so much, Finally, it is possible to make the surface drawing similar to the attached drawing (in color and lines drawn in the horizontal plane)

[T K]

Link photo

https://drive.google.com/file/d/14kltBrMSB2Fd15ppBFhQ_pVlPuXBowER/view?usp=drivesdk

[Karim]

you are welcome, if it works you can consider to accept my answer so that it might help other people as well.

[T K]

Certainly, naturally