Consider the model described in Two van der Pol oscillators coupled via a bath (1).
The current model is using a slightly different notation:
$$\begin{align*}
\dot{\xi}_{1}^{1} &= \dot{x}_1 \\
\dot{\xi}_{2}^{1} &= \dot{x}_2 \\
\dot{\xi}_{1}^{2} &= \dot{x}_3 \\
\dot{\xi}_{2}^{2} &= \dot{x}_4 \\
\dot{\eta}_{1} &= \dot{x}_5
\end{align*}$$
Note that this system is decouplable by static state feedback because the decoupling matrix of this system is
$D_{1}(\xi,\eta)=\left[\matrix{1 &0 \cr 0 &1}\right]$
The authors have proposed the following Yuz and Goodwin type approximate model which is more accurate than the Euler model.
$$\begin{align*}
x_{1,k+1}&=x_{1,k}+T_{x_{2,k}}+\frac{T^2}{2}\{u_{1,k}-x_{1,k}+\epsilon\{1-x_{1,k}^{2}\}x_{2,k}+k(x_{5,k}-x_{1,k})\} \\
x_{2,k+1}&=x_{2,k}+T\{u_{1,k}-x_{1,k}+\epsilon\{1-x_{1,k}^{2}\}x_{2,k}+k(x_{5,k}-x_{1,k})\} \\
x_{3,k+1}&=x_{3,k}+T_{x_{4,k}}+\frac{T^2}{2}\{u_{2,k}-x_{1,k}+\epsilon\{1-x_{3,k}^{2}\}x_{4,k}+k(x_{5,k}-x_{1,k})\} \\
x_{4,k+1}&=x_{4,k}+T_{x_{4,k}}+T\{u_{2,k}-x_{2,k}+\epsilon\{1-x_{3,k}^{2}\}x_{4,k}+k(x_{5,k}-x_{3,k})\} \\
x_{5,k+1}&=x_{5,k}+T\{k(x_{1,k}-x_{5,k})+k(x_{3,k}-x_{5,k})\} \\
y_{1,k}&=x_{1,k} \\
y_{2,k}&=x_{3,k}
\end{align*}$$