Abstract
Low-dimensional chaotic dynamical systems can exhibit many characteristic properties of stochastic systems, such as broad Fourier spectra. They are distinguishable from stochastic processes through finite values for their dimension, Lyapunov exponents, and Kolmogorov-Sinai entropy. We discuss how these characteristic observables are modified in spatiotemporal chaotic systems like. coupled map lattices. We analyze with the help of Lyapunov concepts how the stochastic limit is approached and how these properties can be observed directly through local dimension measurements from reconstructed time series. Finally, we discuss the interaction of spatiotemporal attractors with external noise and possible connections to problems of pattern selection and stability.
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Mayer-Kress, G., Kaneko, K. Spatiotemporal chaos and noise. J Stat Phys 54, 1489–1508 (1989). https://doi.org/10.1007/BF01044730
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DOI: https://doi.org/10.1007/BF01044730