Symptoms of chaos in observed oscillations near a bifurcation with noise

Journal Article · Sat Oct 15 00:00:00 EDT 1988 · J. Chem. Phys.; (United States)

DOI:https://doi.org/10.1063/1.455668· OSTI ID:6843127

Harding, R H; Ross, J

We examine an experimental transition from periodic to aperiodic and back to periodic dynamics in the combustion of acetaldehyde(ACH) in a continuous stirred tank reactor (CSTR) with power spectra, autocorrelation functions, phase portraits, Poincar-acute-accente sections, the Wolf--Swift--Swinney--Vastano (WSSV) method for determining the largest Lyapounov exponent, and the Grassberger--Procaccia (GP) method for determining correlation dimension. Each technique gives some indications of a transition to chaos, but there are discrepancies in that the largest Lyapounov exponent is positive but does not converge and the GP method results in a correlation dimension between one and two for two aperiodic data sets. We explore in instructive detail possible explanations for false indications of chaos by comparing our results with calculations on the Roessler chaotic attractor and the van der Pol periodic attractor modified to examine the effects of uneven point distribution and three types of experimental noise. An uneven distribution of points results in a decreased range of length scales for convergence and a larger required embedding dimension for the GP method, but does not explain our experimental results. Observation noise (a Gaussian noise added to each term in the time series but not entering in the equations of motion) and constraint shift (the motion relaxes to an attractor but a constraint changes monotonically during the course of measurement) added to a periodic attractor both result in a low length scale cutoff below which the attractor dimension does not converge with embedding dimension, and above which it converges to 1. Constraint variation noise (a Gaussian noise is added to each term in the time series and enters into the equations of motion as a stochastic perturbation) does yield correlation dimensions between 1 and 2.

• Research Organization: Department of Chemistry, Stanford University, Stanford, California 94305
• OSTI ID: 6843127
• Journal Information: J. Chem. Phys.; (United States), Vol. 89:8
• Country of Publication: United States
• Language: English

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