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My professor wants us to use the following plotter to plot phase portraits for systems of ODEs but for whatever reason I do not know, neither my professor, nor myself could get this to work on my laptop:

http://comp.uark.edu/~aeb019/pplane.html

So instead, I am trying to use Matlab 2017a (which I personally believe is a better idea and overall better for me).

my first system of (nonlinear) ODEs is as follows: $$x' = 4x - x^3$$ $$y' = y^2 - 3y$$

my second system of (nonlinear) ODEs is as follows: $$x' = 2x -xy$$ $$y' = x^3 - (1/2)y$$

In class we sketched the phase portrait for the second system of nonlinear ODEs by linearizaton via the Jacobian matrix. I can solve these but I am struggling to plot these in Matlab (and haven't made any progress unfortunately)and would absolutely be grateful for some help. Thanks in advance!

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  • $\begingroup$ If you can solve them numerically, then you can surely record $x(t)$ and $y(t)$ for all $t$ you simulate over. Then simply plot those two vectors against each other. Or am I misunderstanding? $\endgroup$ Commented May 3, 2017 at 1:01

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From PPLANE dfield and pplane, the java versions

first

second

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  • $\begingroup$ That is amazing, thank you! If it's too much of a hassle, don't worry about it, but, if you wouldn't mind, would it be possible to see your code? Thanks again $\endgroup$ Commented May 4, 2017 at 16:26
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    $\begingroup$ @Matthew Graham: MATLAB code library for PPLANE: math.rice.edu/%7Edfield/index.html $\endgroup$
    – dantopa
    Commented May 4, 2017 at 16:45

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