Article

Detection of chaotic determinism in time series from randomly forced maps.

Harvard-MIT Division of Health Sciences and Technology, Cambridge, MA, USA.
Physica D Nonlinear Phenomena (impact factor: 1.59). 02/1997; 99:471-86. DOI:10.1016/S0167-2789(96)00159-5 pp.471-86
Source: PubMed

ABSTRACT Time series from biological system often display fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". Despite this effort, it has been difficult to establish the presence of chaos in time series from biological sytems. The output from a biological system is probably the result of both its internal dynamics, 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, i.e., a positive characteristic exponent that leads to sensitivity to initial conditions. 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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Keywords

biological system
 
biological sytems
 
characteristic exponents
 
computer simulations
 
deterministic chaos
 
deterministic components
 
estimation
 
heart rate variability data
 
initial conditions
 
mixed system
 
nonlinear autoregressive model
 
observed probability distribution
 
positive characteristic exponent
 
Time series
 
useful