Coupled chaotic states and apparent noise in experiment and model

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Abstract
We present an experimental and model study of the effect of mass coupling of two similar chaotic states in the Belousov-Zhabotinskii (BZ) reaction. At high coupling strengths the coupled chaotic states become synchronized as shown by a high correlation coefficient. When the coupling strength is decreased, the coupled system passes through a symmetry-breaking transition from synchronized to asynchroneous chaos. At the transition point the direct experimental evaluation of the maximum Lyapunov exponent of the single chaotic system is possible from the coupling strength. At very low coupling strengths the correlation approaches zero. The differences and sums of;the two chaotic time series in each reactor are also investigated. At high and moderate coupling strengths, the differences and the sums are verified to-be deterministically chaotic on the basis of their fractal dimensionalities, for example. However, for weakly coupled (and uncoupled) chaotic states our analysis with state-of-the-art methods shows that the sum and differences behave as if they are stochastic, although the time series of individual reactions always remain deterministically chaotic. The reason for this apparent ''statistical'' behavior at low (and zero ) coupling strengths is the limited number of the experimental (similar to 16 000 data points) and numerical data points available for analysis for large Hausdorff dimensions (D-H > 3.6). Hyperchaos could not be detected in the coupled chaotic BZ systems.

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