I have a 3D differential equation I'm interested in studying the potential landscape using quasipotentials, described in depth in this paper. I need to calculate the potential landscape several times, which makes me need to use a fast method to calculate it, such as a polynomial optimization method. This method assumes the drift of the SDE is of a polynomial form, and my drift term is diffeomorphic to a polynomial system. I was wondering if it's known if there are any differences between potential landscapes between diffeomorphic systems to ensure calculating the potential landscape in the diffeomorphic system will be meaningful for my original system.
