Chaos and Its Reconstruction
Gérard Gouesbet, S. Meunier-Guttin-Cluzel, O. Minard
Nova Science Publishers, Jan 1, 2003 - Technology & Engineering - 320 pages
The editors (of the Universite et Institut National des Sciences Appliquees de Rouen, France) present six chapters exploring the application of chaos theory to such topics as the topological characterisation of attractors and the reconstruction of equations of motion from data. Specific topics include the development of a method of modelling called NARMAX (non-linear autoregressive moving average models with exogenous outputs), a summary of the work of the Centre of Applied Dynamics and Optimisation at the U. of Western Australia), time delayed feedback systems, and global modelling applications to biological data and secure communication.
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Modelling Nonlinear Dynamical Systems From Data
Building Optimal Models of Time Series
Construction of Dynamical Model Equations for Nonautonomous
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Abarbanel algorithm applications approach approximation basis functions behaviour Belousov-Zhabotinskii reaction Bifurcation and Chaos bifurcation diagrams Casdagli chaotic attractors chaotic systems chaotic time series coefficients computed control parameters coordinates correlation dimension delay derivatives deterministic diffeomorphism differential equations discussed driving dynamical systems embedding dimension entropies equivariant error evaluate example experimental data Figure filter first-return map forecasting global models global reconstruction global vector field Gouesbet identification invariant measure iteration Journal of Bifurcation Judd L. A. Aguirre Letellier Lorenz system Lyapunov exponents Maquet mathematical Menard method model class model structure multiple shooting NARMAX noise nonlinear dynamics nonlinear models observations obtained optimal original system oscillator parameter estimation phase portrait phase space Phys Physics Letters points prediction predictor problem properties rational functions Rossler system S. A. Billings Sceller Section signal smoothing spline standard embeddings strange attractors symbolic dynamics synchronization template time-delay trajectory upos values vector field reconstructions