Let $a \in \mathbb{R}$. If there exists a function $f ( x )$ with domain $\mathbb{R}$ that satisfies both ``for any $x _ { 0 } \in \mathbb{R}$, the value of $f \left( x _ { 0 } \right)$ is either $x _ { 0 } ^ { 2 }$ or $x _ { 0 }$'' and ``the equation $f ( x ) = a$ has no real solutions'', find the range of $a$ as $\_\_\_\_$