How to shadow noisy chaos

John Maddox

doi:10.1038/347613a0

Using the Lyapunov Exponent as a Practical Test for Noisy Chaos

SSRN Electronic Journal ◽

10.2139/ssrn.970074 ◽

2007 ◽

Cited By ~ 2

Author(s):

Ahmed Ben Saïda

Keyword(s):

Lyapunov Exponent ◽

Practical Test ◽

Noisy Chaos

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Symbolic dynamics of noisy chaos

Physica D Nonlinear Phenomena ◽

10.1016/0167-2789(83)90127-6 ◽

1983 ◽

Vol 7 (1-3) ◽

pp. 201-223 ◽

Cited By ~ 126

Author(s):

J.P. Crutchfield ◽

N.H. Packard

Keyword(s):

Symbolic Dynamics ◽

Noisy Chaos

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A kind of noise-induced transition to noisy chaos in stochastically perturbed dynamical system

Acta Mechanica Sinica ◽

10.1007/s10409-012-0084-9 ◽

2012 ◽

Vol 28 (5) ◽

pp. 1416-1423 ◽

Cited By ~ 6

Author(s):

Chun-Biao Gan ◽

Shi-Xi Yang ◽

Hua Lei

Keyword(s):

Dynamical System ◽

Noisy Chaos ◽

Stochastically Perturbed

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A Note on Noisy Chaos

Journal of the Royal Statistical Society Series B (Methodological) ◽

10.1111/j.2517-6161.1994.tb01979.x ◽

1994 ◽

Vol 56 (2) ◽

pp. 301-311 ◽

Cited By ~ 2

Author(s):

K. S. Chan ◽

H. Tong

Keyword(s):

Noisy Chaos

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Detection of “Noisy” Chaos in a Time Series

Methods of Information in Medicine ◽

10.1055/s-0038-1636859 ◽

1997 ◽

Vol 36 (04/05) ◽

pp. 294-297 ◽

Cited By ~ 1

Author(s):

J. K. Kanters ◽

R. J. Cohen ◽

N.-H. Holstein-Rathlou ◽

K. H. Chon

Keyword(s):

Time Series ◽

Deterministic Chaos ◽

Mixed System ◽

Internal Dynamics ◽

Characteristic Exponents ◽

Nonlinear Autoregressive Model ◽

Deterministic Components ◽

Nonlinear Autoregressive ◽

Noisy Chaos ◽

Variability Data

Abstract:Time series from biological system often displays fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely “noise”. The output from most biological systems is probably the result of both the internal dynamics of the systems, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series, and if this determinism has chaotic attributes. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data.

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