How plot a polar phase-portrait with matlab

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 ?

Answer 1

[Cristóbal Álvarez Contreras]

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!