2

$$\dot x = -2x-y^2$$ $$\dot y = -y-x^2$$

$(0,0)$ is an obvious attractive fixed point, and I'll only look at this one.

I need to get the maximal radius $r > 0$ for a ball centered on the origin so that ball is still included in the basin of attraction.

I used $x^2+y^2$ as my Lyapunov function and determined that its domain of validity, defined by $\dot L < 0$, is given by $ x > -1$ and $y > -2$. But since it is an arbitrary choice I'm not sure I can conclude something from that.

Rodrigo de Azevedo
  • 23,223
alphaslow
  • 21
  • 3
    Well, there is another equilibrium point, so the radius cannot be larger than the distance between the origin and that point. – Michael Nov 19 '15 at 00:27
  • 1
    See https://math.stackexchange.com/questions/2576408/lyapunov-function-and-an-open-disk-inside-the-basin-of-0-0/3799731#3799731 – Cesareo Aug 23 '20 at 13:50

0 Answers0