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!

回答(2 个)

Ameer Hamza
Ameer Hamza 2020-4-19
编辑:Ameer Hamza 2020-4-19
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
  2 个评论
Frantisek Stloukal
Frantisek Stloukal 2021-4-29
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 2021-5-5
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 2022-1-26
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

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