14. If the system of equations concerning $x$ and $y$
$$
\left\{\begin{array}{l}
\sin x=m \sin ^{3} y, \\
\cos x=m \cos ^{3} y
\end{array}\right.
$$

has real solutions, then the range of positive real number $m$ is
$\qquad$.
14. $[1,2]$.

Squaring both equations and eliminating $x$, we get
$$
\begin{array}{l}
\sin ^{2} 2 y=\frac{4}{3}\left(1-m^{2}\right) \in[0,1] \\
\Rightarrow 1 \leqslant m^{2} \leqslant 2 .
\end{array}
$$

Conversely, when $1 \leqslant m^{2} \leqslant 2$, there exists $\left(x_{0}, y_{0}\right)$ that satisfies the equations.
Therefore, the positive real number $m \in[1,2]$.