Need to make surf plot in ode45

Question

Suganya G 2021-10-30

0
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https://ww2.mathworks.cn/matlabcentral/answers/1575133-need-to-make-surf-plot-in-ode45

编辑： Chris 2021-10-30

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 

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Answer 1

Chris 2021-10-30

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1575133-need-to-make-surf-plot-in-ode45#answer_820118

编辑：Chris 2021-10-30

在 MATLAB Online 中打开

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

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Walter Roberson 2021-10-30

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 2021-10-30

It is working. Thanks a lot!!

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Answer 2

Walter Roberson 2021-10-30

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1575133-need-to-make-surf-plot-in-ode45#answer_820113

在 MATLAB Online 中打开

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

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Suganya G 2021-10-30

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!!

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Need to make surf plot in ode45

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