Conference proceeding
Topological analysis of chaotic time series
Proceedings of SPIE, v 3165(1)
13 Oct 1997
Abstract
Topological methods have recently been developed for the classification, analysis, and synthesis of chaotic time series. These methods can be applied to time series with a Lyapunov dimension less than three. The procedure determines the stretching and squeezing mechanisms which operate to create a strange attractor and organize all the unstable periodic orbits in the attractor in a unique way. Strange attractors are identified by a set of integers. These are topological invariants for a two dimensional branched manifold, which is the infinite dissipation limit of the strange attractor. It is remarkable that this topological information can be extracted from chaotic time series. The data required for this analysis need not be extensive or exceptionally clean. The topological invariants: (1) are subject to validation/invalidation tests; (2) describe how to model the data; and (3) do not change as control parameters change. Topological analysis is the first step in a doubly discrete classification scheme for strange attractors. The second discrete classification involves specification of a 'basis set' set of periodic orbits whose presence forces the existence of all other periodic orbits in the strange attractor. The basis set of orbits does change as control parameters change. Quantitative models developed to describe time series data are tested by the methods of entrainment. This analysis procedure has been applied to analyze a number of data sets. Several analyses are described.
Metrics
Details
- Title
- Topological analysis of chaotic time series
- Creators
- Robert Gilmore - Drexel University
- Publication Details
- Proceedings of SPIE, v 3165(1)
- Conference
- Applications of Soft Computing
- Publisher
- Society of Photo-Optical Instrumentation Engineers (SPIE)
- Resource Type
- Conference proceeding
- Language
- English
- Academic Unit
- [Retired Faculty]
- Web of Science ID
- WOS:A1997BJ78S00024
- Scopus ID
- 2-s2.0-0040125168
- Other Identifier
- 991019167984704721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Web of Science research areas
- Computer Science, Artificial Intelligence
- Computer Science, Interdisciplinary Applications
- Optics