  We use nonlinear signal processing techniques, based on artificial neural
networks, to construct an empirical mapping from experimental Rayleigh-Benard
convection data in the quasiperiodic regime. The data, in the form of a
one-parameter sequence of Poincare sections in the interior of a mode-locked
region (resonance horn), are indicative of a complicated interplay of local and
global bifurcations with respect to the experimentally varied Rayleigh number.
The dynamic phenomena apparent in the data include period doublings, complex
intermittent behavior, secondary Hopf bifurcations, and chaotic dynamics. We
use the fitted map to reconstruct the experimental dynamics and to explore the
associated local and global bifurcation structures in phase space. Using
numerical bifurcation techniques we locate the stable and unstable periodic
solutions, calculate eigenvalues, approximate invariant manifolds of saddle
type solutions and identify bifurcation points. This approach constitutes a
promising data post-processing procedure for investigating phase space and
parameter space of real experimental systems; it allows us to infer phase space
structures which the experiments can only probe with limited measurement
precision and only at a discrete number of operating parameter settings.
