  Recently Herzog and Mattingly have shown that a $\mathbb{C}$-valued
polynomial ODE which admits finite-time blow-up solutions may be stabilized by
the addition of $\mathbb{C}$-valued Brownian noise. In this paper we extend
their problem to a $\mathbb{C}^2$-valued system of coupled ODEs that also
admits finite-time blow-up solutions. We show analytically and numerically that
stabilization can be achieved in our setting by adding a suitable Brownian
noise, and that the resulting system of SDEs is ergodic. The proof uses
Girsanov theorem to effect a time change from our $\mathbb{C}^2$-system to a
quasi-$\mathbb{C}$-system similar to the one studied by Herzog and Mattingly.
