How does one plot phase portraits for systems of differential equations?

I'm sort of new to this whole process and a lof of my homework for diff eq's asks for us to use technology to plot some of the solutions.

We just started last week on system of diff eq's and I wanted to learn how to do this with MATLAB. Be easy on me as I have very limited knowledge of the language.

The example I have on hand of something I've been asked to plot is the following:

Where x is a function of t.

Any help would be greayly appreciated. Thank in advance!

Answer 1

[Ameer Hamza]

See this: http://matlab.cheme.cmu.edu/2011/08/09/phase-portraits-of-a-system-of-odes/ to understand how to make phase portraits in MATLAB. The following shows an example without using for-loop for your equations.

[X1,X2] = meshgrid(-5:0.5:5);

xs = arrayfun(@(x,y) {odeFun([],[x,y])}, X1, X2);
x1s = cellfun(@(x) x(1), xs);
x2s = cellfun(@(x) x(2), xs);

quiver(x1s, x2s)
xlabel('x_1')
ylabel('x_2')
axis tight equal;

function dxdt = odeFun(t,x)
    dxdt(1) = 5*x(1)-9*x(2);
    dxdt(2) = 1*x(1)-5*x(2);
end

[Frantisek Stloukal]

Hi, how do i get the axis in the right place ? The stable point should be [0,0] not [11,11]... Thanks for answer.

[Ahsan Mujtaba]

In this question, I wanted to ask that the all the possible initial consitions are being plotted?

Answer 2

[Brian Hong]

There are also apps that you can use to plot your phase portrait. Here's one that we created recently: https://www.mathworks.com/matlabcentral/fileexchange/91705-phase-plane-and-slope-field-apps