$$\begin{align}\dot{x}_{0}&=- x_{0}^{4} + x_{0}^{3} + x_{0}^{2} \cdot x_{1}^{2} - x_{0} \cdot x_{1}^{2} - x_{1}^{4}\\\dot{x}_{1}&=x_{0}^{2} \cdot x_{1} - 1.0 \cdot x_{1}^{3}\end{align}$$
no description available
non-linear
$$\begin{align}x_{0}(0)&\subset~\left[ 0.2, 1.0\right]\\x_{1}(0)&\subset~\left[ 0.5, 1.0\right]\end{align}$$
No exact solution provided.
[untested]
$$\begin{align}x_{0}(0)&=1.0\\x_{1}(0)&=1.0\end{align}$$
* rounded (non-rigorously) to 5 decimal places to preserve screen real estate.