$$\begin{align}\dot{x}_{0}&=- x_{0}^{3} + x_{1} \cdot x_{2} - 2.0 \cdot x_{1}\\\dot{x}_{1}&=- x_{0} \cdot x_{2} + x_{0} - x_{1}^{3}\\\dot{x}_{2}&=x_{0} \cdot x_{1} - x_{2}^{3}\end{align}$$
no description available
non-linear
$$\begin{align}x_{0}(0)&\subset~\left[ 0.5, 1.5\right]\\x_{1}(0)&\subset~\left[ 0.8, 1.2\right]\\x_{2}(0)&\subset~\left[ 0.4, 1.6\right]\end{align}$$
No exact solution provided.
[untested]
$$\begin{align}x_{0}(0)&=1.0\\x_{1}(0)&=1.0\\x_{2}(0)&=1.0\end{align}$$
* rounded (non-rigorously) to 5 decimal places to preserve screen real estate.