Revealing dynamical systems and their bifurcation structure hidden by dynamical noise

This paper discusses bifurcation diagram reconstruction [1, 2] and shows by a numerical experiment that the correct bifurcation diagram of a dynamical system can be reconstructed from the signal of a chaotic dynamical system perturbed by a sufficiently large dynamical noise. It is also verified that the predictor derived using the proposed method not only can approximate the dynamical rules on the attractor, but also has an excellent global approximation ability on a sufficiently large open set containing the attractor. (C) 1997 Scripta Technica, Inc.