TIME-SERIES ANALYSIS OF PHYSICAL SYSTEMS POSSESSING HOMOCLINICITY

Homoclinic orbits (and heteroclinic cycles) play an important role in the study of dynamical systems. There is now an established theoretica l framework for investigating the often complicated sequences of bifur cations that can exist within small regions of parameter space close t o the conditions for homoclinicity. It is the eigenvalues of the saddl e point that determine this behaviour. In this paper a method is prese nted whereby an experimentalist with access to a single experimental t ime series taken from a system close to homoclinicity can estimate the se eigenvalues. Appropriate nonlinear models may then be constructed a nd analysed that give predictions for the local behaviour of the syste m.