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

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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!

Answers (2)

Ameer Hamza
Ameer Hamza on 19 Apr 2020
Edited: Ameer Hamza on 19 Apr 2020
See this: 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)
axis tight equal;
function dxdt = odeFun(t,x)
dxdt(1) = 5*x(1)-9*x(2);
dxdt(2) = 1*x(1)-5*x(2);
Frantisek Stloukal
Frantisek Stloukal on 29 Apr 2021
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
Ahsan Mujtaba on 5 May 2021
In this question, I wanted to ask that the all the possible initial consitions are being plotted?

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Brian Hong
Brian Hong on 26 Jan 2022
There are also apps that you can use to plot your phase portrait. Here's one that we created recently:


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