Prokaryotic autoregulatory gene network

\[dX_t = b(X_t)dt + \sigma(X_t) dW_t,\]

where

\[b(x):=\left(\begin{matrix} c_3 x^{[4]} - c_7 x^{[1]}\\ c_4 x^{[1]} + 2f(x) - c_8 x^{[3]}\\ g(x)-f(x)\\ g(x) \end{matrix}\right)\]

with

\[\begin{align*} f(x)&:=c_6 x^{[3]}-0.5c_5x^{[2]}(x^{[2]}-1)\\ g(x)&:=c_2(K-x^{[4]})-c_1 x^{[3]}x^{[4]} \end{align*}\]

and

\[\sigma(x)\]