Determining boundary of basins of attraction Let's say that I have a dynamical system that displays multiple stable states with corresponding basins of attraction. The Lyapunov function for the system is not known. 
Is there an analytic or semi-analytic method to locate the edges of basins, ie where one basin ends and another begins? In a system that has many such basins, there might be special points where several basins meet (I'm thinking of points at which very small changes in initial conditions can leave the system in one of several possible equilibrium states). Is there anything I can do here given that I don't explicitly know the Lyapunov function?
My system doesn't have fractal basin boundaries or anything unusual like that. It's a system of four dependent variables as well as time.
Thank you!

The short answer is no -- there is no such general method in dimension >2. Sometimes you can compute one-dimensional separatrices using Melnikov methods, but nothing more. There are also numerical techinques but analysis could be done only for some very specific systems.
Usually you can not determine even one single domain of attraction analytically.
