Smoothness Implies Determinism: A Method to Detect It in Time Series
- 22 August 1994
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 73 (8) , 1091-1094
- https://doi.org/10.1103/physrevlett.73.1091
Abstract
Continuity on an embedded phase space is enough to imply determinism in time series. Also, it is possible to define infinitely many arbitrary vector fields over an attractor. We exploit this arbitrariness to generate a detector of smoothness and therefore of determinism in time series. We report results of numerical studies of both flow and map examples and of a chaotic experimental system.Keywords
This publication has 7 references indexed in Scilit:
- Recognizing determinism in a time seriesPhysical Review Letters, 1993
- Method to distinguish possible chaos from colored noise and to determine embedding parametersPhysical Review A, 1992
- Local-geometric-projection method for noise reduction in chaotic maps and flowsPhysical Review A, 1992
- Direct test for determinism in a time seriesPhysical Review Letters, 1992
- Nonlinear forecasting as a way of distinguishing chaos from measurement error in time seriesNature, 1990
- Experimental observation of crisis-induced intermittency and its critical exponentPhysical Review Letters, 1989
- Geometry from a Time SeriesPhysical Review Letters, 1980