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I have a dynamical system $$ \left\{ \begin{array}{rcl} \dot {x_1} & = & -\frac{2x_{1}}{(1+x_{1}^2)^2} - \frac{2x_2}{(1+x_2^2)^2} \\ \dot {x_2} & = & 2x_1 - \frac{2 x_2}{(1+x_2^2)^2} \end{array} \right. $$ Here $(x_1, x_2) \in \mathbb{R}^2$. Zero solution is an attractor, but I know that zero solution is not a global attractor. How to show this analitically (without writing a program)? Any ideas are welcome.

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Why is it not a global attractor? How do you know that? – Pantelis Sopasakis Dec 4 '12 at 2:28
@PantelisSopasakis I wrote a program. Furthermore, it is a homework problem! – Nimza Dec 4 '12 at 7:14

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