RETRIEVING DYNAMICAL INVARIANTS FROM CHAOTIC DATA USING NARMAX MODELS

摘要: This paper is concerned with the estimation of dynamical invariants from relatively short and possibly noisy sets chaotic data. In order to overcome difficulties associated size quality data records, a two-step procedure investigated. Firstly NARMAX models are fitted Secondly, such used generate longer cleaner time sequences which as Lyapunov exponents, correlation dimension, geometry attractors, Poincare maps bifurcation diagrams can be estimated relative ease. An additional advantage this that because global have simple structure, amenable for analysis. It shown location stability fixed points original systems analytically recovered identified models. A number examples included use logistic Henon maps, Duffing modified van der Pol oscillators, Mackey-Glass delay system, Chua’s circuit, Lorenz Rossler attractors. The these provided including discrete multivariable double scroll, attractors reconstruct trajectories in three-dimensional state space.