7. Reconstructing equations of motion

We assume that the system under consideration is deterministic, and that the only information available about the system is a time series x(t) of a scalar variable x. We propose to reconstruct equations of motion that reproduce the dynamics from the observed scalar series alone. When this goal is achieved, a phenomenological model is obtained for the observed variable, as well as for other unobserved dynamic variables. We will confine ourselves to the global reconstruction of vector fields. For application reconstruction, see