Titration of Chaos with Added Noise

Deterministic chaos has been implicated in numerous natural and man-made complex phenomena ranging from quantum to astronomical scales and in disciplines as diverse as meteorology, physiology, ecology, and economics. However, the lack of a definitive test of chaos vs. random noise in experimental ti...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS 2001-06, Vol.98 (13), p.7107-7112
Main Authors: Poon, Chi-Sang, Barahona, Mauricio
Format: Article
Language:English
Subjects:
Algorithms
Biological Sciences
Biology
Chaos theory
Datasets
Determinism
Electricity
Equivalence points
Humans
Information retrieval noise
Mathematics
Noise
Noise measurement
Nonlinear Dynamics
Nonlinearity
Physical Phenomena
Physical Sciences
Physics
Signal noise
Socioeconomic Factors
Titration
White noise
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Summary:Deterministic chaos has been implicated in numerous natural and man-made complex phenomena ranging from quantum to astronomical scales and in disciplines as diverse as meteorology, physiology, ecology, and economics. However, the lack of a definitive test of chaos vs. random noise in experimental time series has led to considerable controversy in many fields. Here we propose a numerical titration procedure as a simple "litmus test" for highly sensitive, specific, and robust detection of chaos in short noisy data without the need for intensive surrogate data testing. We show that the controlled addition of white or colored noise to a signal with a preexisting noise floor results in a titration index that: (i) faithfully tracks the onset of deterministic chaos in all standard bifurcation routes to chaos; and (ii) gives a relative measure of chaos intensity. Such reliable detection and quantification of chaos under severe conditions of relatively low signal-to-noise ratio is of great interest, as it may open potential practical ways of identifying, forecasting, and controlling complex behaviors in a wide variety of physical, biomedical, and socioeconomic systems.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.131173198