Approximating stable and unstable manifolds in experiments.
We introduce a procedure to reveal invariant stable and unstable manifolds, given only experimental data. We assume a model is not available and show how coordinate delay embedding coupled with invariant phase space regions can be used to construct stable and unstable manifolds of an embedded saddle. We show that the method is able to capture the fine structure of the manifold, is independent of dimension, and is efficient relative to previous techniques.
Triandaf
Ioana
I
Code 6792, Plasma Physics Division, Naval Research Laboratory, Washington, DC 20375, USA.
Bollt
Erik M
EM
Schwartz
Ira B
IB