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

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]

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]

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.

Answer 1

[Ameer Hamza]

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]

Thank you so much!!!!

[Ameer Hamza]

I am glad to be of help!