Figure 1

Two-dimensional models with $\mathbf{(}{\mathit{\sigma }}_{\mathbf{1}}\mathbf{,}{\mathit{\sigma }}_{\mathbf{2}}\mathbf{)}\mathbf{=}\mathbf{(}\mathbf{1}\mathbf{,}\mathbf{-}\mathbf{1}\mathbf{)}$. The dark circles denote initial conditions (see Examples 3.2, 3.6, and 3.7 for details). (a) $r_1{a}_{21}-r_2{a}_{11}<0$ and the limits of the four trajectories are $(\frac{r_1}{a_{11}},0)=(10,0)$. (b) $r_1{a}_{21}-r_2{a}_{11}>0$. The solutions of equation (2.1) rotate finitely many times around the limit $\mathit{\theta }=({\theta }_1,{\theta }_2)=(1.25,0.25)$. (c) $r_1{a}_{21}-r_2{a}_{11}>0$. The solutions of equation (2.1) rotate infinitely many times around the limit $\mathit{\theta }=(1.287,28.713)$.