Introduction

International Journal of Bifurcations and Chaos, Vol. 8, Nr. 5(1998) 899-914

A General Form for Global Dynamical Data Models for Three-Dimensional Systems

Claudia S. M. Lainscsek¹, Ferdinand Schürrer¹ and James B. Kadtke²

The information contained in a scalar time series and its numerical derivatives is used to construct a global model for the underlying dynamical system, using a model transformation presented previously. Here, however, we analytically determine the most general form for the transformed model in the case of a three-dimensional model ansatz. We then test this method by reconstructing global models for known chaotic dynamical systems, and comparing correlation and topological measures of the re-constructed and original systems. We also do a preliminary investigation of a real data set consisting of the sunspot number over the last 200 years.

 

• Introduction
• Global Modeling by means of a Transformed System
• Global Modeling of Simulated Systems
• Lorenz System
• Rössler System
• Global Modeling of a Real System - Sunspots
• Estimates of the Parameters for the SVD Derivatives
• Dimension Estimates
• Previous Dynamical Analysis
• Global Modeling of Sunspot Data
• Conclusion
• Most General Transformation
• Singular Value Decomposition (SVD)
• SVD for Solving an Overdetermined System of Linear Equations
• References
• About this document ...

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