Abstract

Introduction 2. Spatiotemporal Data 3. Dynamical Systems Concepts 4. Karhunen-Love Decomposition 5. Overview of kltool 6. Examples 7. Future Directions 8. Summary Bibliography Appendix: Galrkin Projection for Kuramoto-Sivashinsky PDE 1. Introduction The quantitative analysis of low-dimensional chaotic dynamical systems has been an active area of research for many years. Up until now, most work has concentrated on the analysis of time series data from laboratory experiments and numerical simulations. Examples include Rayleigh-Bnard convection, Couette-Taylor fluid flow, and the Belousov-Zhabotinskii chemical reaction [Libchaber, Fauve & Laroche '83], [Roux '83] and [Swinney '84]. The key idea is to reconstruct a representation of the underlying attractor from the time series. (The time-delay embedding method [Takens '81] is one popular approach). Given the reconstructed attractor, it is possible to estimate various properties of the dynamics - Lyapunov e

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