\begin{align}
\frac{\mathrm{d} x\left( t \right)}{\mathrm{d}t} &= \frac{\left(  - x\left( t \right) + y\left( t \right) \right) \frac{\mathrm{d}}{\mathrm{d}t} \left( x\left( t \right) - y\left( t \right) \right) \sigma}{\frac{\mathrm{d} z\left( t \right)}{\mathrm{d}t}} \\
0 &=  - y\left( t \right) + \frac{1}{10} x\left( t \right) \left(  - z\left( t \right) + \rho \right) \sigma \\
\frac{\mathrm{d} z\left( t \right)}{\mathrm{d}t} &= \left( y\left( t \right) \right)^{\frac{2}{3}} x\left( t \right) - z\left( t \right) \beta
\end{align}
