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How plot a polar phase-portrait with matlab

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etienne genier
etienne genier on 4 Jan 2017
Hi,
I have for exempl the following systems :
r'=r(1-r²)(4-r²), theta'=2r-1; or r'=r^3-4r, theta'=1;
and I want to plot the polar phase portrait of this system.
I sucess to plot the phase portrait in cartesian coordinates with for exempl :
[x1, x2]=meshgrid(-1:0.1:1,-1:0.1:1);
x1dot=x1-x2-x1.*(x1.^2+x2.^2);
x2dot=x1+x2-x2.*(x1.^2+x2.^2);
quiver(x1,x2,x1dot,x2dot)
But not in polar coordinates
Someone can help me ?

Answers (1)

Cristóbal Álvarez Contreras
Edited: Cristóbal Álvarez Contreras on 11 May 2021
Hi etienne, this question have a lot of time here and i did have the same question, i hope that this answer can help the community.
A solution is directly write your system in the cartesian plane, i.e
derive the equalities and replace the θ', and . After apply quiver and you have the phase portrait. A very good app to do it is https://la.mathworks.com/matlabcentral/fileexchange/81026-phase-portrait-plotter
regards!

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