We show that the addition of a suitable Stratonovich noise prevents the explosion for ODEs with drifts of super-linear growth, in dimension $d\ge 2$. We also show the existence of an invariant measure and the geometric ergodicity for the corresponding SDE.
"Non-explosion by Stratonovich noise for ODEs." Electron. Commun. Probab. 25 1 - 10, 2020. https://doi.org/10.1214/20-ECP347