Before revision:  Here we present a numerical method for decomposing differential equations of any size in two terms, one that has an associated potential (the gradient term), and another one that lacks it ( the non-gradient term ) . In regions of the state space where the magnitude of the non-gradient term is small compared to the gradient part, we can still make approximate use of the concept of potential .
After revision:  Here we use an analogy with art to provide an accessible explanation of why this happens. Additionally, we introduce a numerical method for decomposing differential equations of any size in two terms, one that has an associated potential (the gradient term), and another one that lacks it ( the non-gradient term ) . In regions of the state space where the magnitude of the non-gradient term is small compared to the gradient part, we can still make approximate use of the concept of potential .