Abstract
An increasing body of experimental evidence supports the belief that random behavior observed in a wide variety of physical systems is due to underlying deterministic dynamics on a low-dimensional chaotic attractor. The behavior exhibited by a chaotic attractor is predictable on short time scales and unpredictable (random) on long time scales. The unpredictability, and so the attractor’s degree of chaos, is effectively measured by the entropy. Symbolic dynamics is the application of information theory to dynamical systems. It provides experimentally applicable techniques to compute the entropy, and also makes precise the difficulty of constructing predictive models of chaotic behavior. Furthermore, symbolic dynamics offers methods to distinguish the features of different kinds of randomness that may be simultaneously present in any data set: chaotic dynamics, noise in the measurement process, and fluctuations in the environment.
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Crutchfield, J.P., Packard, N.H. (1982). Noise Scaling of Symbolic Dynamics Entropies. In: Haken, H. (eds) Evolution of Order and Chaos. Springer Series in Synergetics, vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-68808-9_19
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DOI: https://doi.org/10.1007/978-3-642-68808-9_19
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