 The algebra necessary for this example is easily carried out by a web service that computes normal form coordinate transforms of systems of differential equations, autonomous or non-autonomous, deterministic or stochastic.Consider the 2D system in variables formula_21 evolving according to the pair of coupled differential equations

By direct computation it can be seen that the only equilibrium of this system lies at the origin, that is formula_23.The coordinate transform, formula_24 where formula_25, given by

is a smooth map between the original formula_21 and new formula_25 coordinates, at least near the equilibrium at the origin.