How to plot this phase portrait correctly?

The following ODE describes a nonlinear mechanical system:

where are numerically given system parameters.

I have to plot the phase portrait of this ODE. I tried the following:

I tried the following code:

clear all;
clc;

%data:
l=0.1;
a=0.06;
m=1;
s=1200;

[x,y]=meshgrid(-0.12:.0005:0.12, -0.12:.0005:0.12);
dx=y;
dy=-(s/m)*x.*(1-l*(sqrt(x.^2+a^2))).^(-1);
streamslice(x,y,dx,dy);
title('Phase portrait')
axis tight equal

The system has 3 equilibrium points: in (0;0) there is a saddle, in (0.08;0) there is a centre, and in (-0.08;0) there is also a centre. So the phase portrait should look like the following:

Yet, Matlab gives me the following:

This isn't look good. What could be the problem, and how should I fix my code, to get a better result?

Answer 1

[Ameer Hamza]

You wrote the equation for dy wrong. Also, the range of y-values is also small. Try this

clear all;
clc;
%data:
l=0.1;
a=0.06;
m=1;
s=1200;
[x,y]=meshgrid(-0.12:0.01:0.12, -1:0.2:1);
dx = y;
dy = -(s/m)*x.*(1-l./sqrt(x.^2+a^2));
streamslice(x, y, dx, dy, 'filled');
title('Phase portrait')
axis tight

[Levente Kis]

Thank you! It works.

Although the arrows looks pretty ugly, is there a solution for that?

[Ameer Hamza]

You can try quiver instead of streamslice. For example,

clear all;
clc;
%data:
l=0.1;
a=0.06;
m=1;
s=1200;
[x,y]=meshgrid(-0.15:0.01:0.15, -1:0.2:1);
dx = y;
dy = -(s/m)*x.*(1-l./sqrt(x.^2+a^2));
streamslice(x, y, dx, dy);
% hold on
quiver(x, y, dx, dy);
title('Phase portrait')
axis tight