\left\{x'(t)=-y(t) \left(x(t)^2+y(t)^2\right),y'(t)=\left(\begin{array}{cc} \{ & \begin{array}{cc} x(t)^2+y(t)^2 & x(t)^2+y(t)^2\geq 2 x(t) \\ \left(x(t)^2+y(t)^2\right) \left(\frac{x(t)}{2}-\frac{y(t)^2}{2 x(t)}\right) & \text{True} \\\end{array} \\\end{array}\right)\right\}