# Phase portrait of a 2 dimensional system that converges to a unit circle

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Penglin Cai on 5 Jun 2020 at 17:30
Commented: Ameer Hamza on 6 Jun 2020 at 8:56
The dynamical system contains two ODES:
dxdt=(1-(x.^2+y.^2)).*x-3.*y.*(x.^2+y.^2);
dydt=(1-(x.^2+y.^2)).*y+3.*x.*(x.^2+y.^2);
where :
x(t)=cos(3*t);
y(t)=sin(3*t);
This system has a unstable solution: x(t)=y(t)=0.
I want to produce a phase portrait of this system which will look like this: Please help me. I do not know what code to use in order to produce this plot. The aatachment is the question. Thank you for the help!!!!

David Goodmanson on 6 Jun 2020 at 6:15
Hi Penglin,
is this a homework problem, and if so what kind of information have they given you about how you can produce this plot in Matlab?
Penglin Cai on 6 Jun 2020 at 8:17
Yes, the picture below is the original question, l really do not know what command to use in order to plot this graph. Thank you for your help.

Ameer Hamza on 6 Jun 2020 at 8:35
Edited: Ameer Hamza on 6 Jun 2020 at 8:36
try this
dx_dt = @(x,y) (1-(x.^2+y.^2)).*x-3.*y.*(x.^2+y.^2);
dy_dt = @(x,y) (1-(x.^2+y.^2)).*y+3.*x.*(x.^2+y.^2);
[x, y] = meshgrid(-2:0.02:2, -2:0.02:2);
dx = dx_dt(x, y);
dy = dy_dt(x, y);
streamslice(x, y, dx, dy);
axis tight
axis equal
hold on
fplot(@(t) cos(3*t), @(t) sin(3*t), [0, 2*pi/3], 'Color', 'r', 'LineWidth', 2) Penglin Cai on 6 Jun 2020 at 8:52
Thank you so much!!!!
Ameer Hamza on 6 Jun 2020 at 8:56
I am glad to be of help!