Matlab tool to plot 3d phase portrait

Question

Shreshtha Chaturvedi 2024-5-11

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https://ww2.mathworks.cn/matlabcentral/answers/2117751-matlab-tool-to-plot-3d-phase-portrait

回答： Sam Chak 2024-5-13

I have the following system of differential equations

x' = -alpha0 * x + beta0 * x * y; 
y' = alpha1 * y - beta1 * x * y;
z' = -alpha2 * (z - 5.5)^3 - beta2 * x * y;

I wanted to take a look at the phase portrait of this system for various values of the coefficients. Is there an inbuilt matlab tool that can do that?

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Answer 1

Sam Chak 2024-5-13

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在 MATLAB Online 中打开

Hi @Shreshtha Chaturvedi

If you want to use multiple slider widgets for alpha and beta to visualize the interactive 3D phase portrait, then you need to use the Graphical User Interface Design Environment or the App designer to create your desired graphical user interface (GUI).

help GUIDE
  Graphical user interface design environment
  MATLAB Version 24.1 (R2024a) 19-Nov-2023 
 
  GUIDE functions.
    guide       	- Open the GUI Design Environment.

    Documentation for matlab/guide
       doc guide

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Answer 2

Steven Lord 2024-5-12

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Use odeset to set the OutputFcn option to @odephas3. See the ballode or orbitode example files for a demonstration of how to use the OutputFcn option, though I believe those use @odeplot and @odephas2 instead of @odephas3.

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Sam Chak 2024-5-12

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Hi @Shreshtha Chaturvedi

@Steven Lord suggested calling '@odephas3' to generate the 3D phase plot. Is this what you were looking for? The 'quiver3' function is used for plotting a 3D vector field, which can be challenging for humans to visualize when projected on a static 2D plane. However, on your MATLAB machine, you can manually rotate the view using your mouse.

initX = [0 0 0

0 0 1

1 0 0

1 0 1

1 1 0

1 1 1];

tspan = [0 10];

X0 = initX(3,:); % test different initial values

opts = odeset('OutputFcn', @odephas3); % <-- insert this

[t, X] = ode45(@ode, tspan, X0, opts);

%% Differential Equations

function dX = ode(t, X)

dX = zeros(3, 1);

x = X(1);

y = X(2);

z = X(3);

alpha0 = 1;

beta0 = 1;

alpha1 = 1;

beta1 = 1;

alpha2 = 1;

beta2 = 1;

dX(1) = -alpha0 * x + beta0 * x * y;

dX(2) = alpha1 * y - beta1 * x * y;

dX(3) = -alpha2 * (z - 5.5)^3 - beta2 * x * y;

end

Shreshtha Chaturvedi 2024-5-12

编辑：Shreshtha Chaturvedi 2024-5-12

I see. However, I just wanted to see how the solutions behave via the phase portrait, not plot the actual solutions by solving it using ode45. As far as plotting the solutions are concerned, I have separately used Euler's method to solve the ode, as one cannot specify a particular time step in ode45. I am just plotting that solution using plot3, but I will check this out too. My original doubt however, is whether there exists any interactive tool, a widget of sorts, through which we can change the coefficients and obtain various phase portraits.

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