Moderate# Solutions that Oscillate as $t\rightarrow\infty$

DIFFEQ-NVYHCE

Consider the linear system:

$$\begin{eqnarray*}u_1&=u_1+u_2\\\ \\\ u_2&=au_1+u_2\end{eqnarray*}$$

For what values of $a$ does this system have solutions that oscillate as $t\rightarrow\infty$?