Abstract
The theory of nonlinear systems has become increasingly useful and relevant to the study of empirical dynamics. When a system produces irregularity in one or more of its variables, it is of interest whether this behavior results from randomness (meaning that the number of degrees of freedom is infinite) or whether a finite, and possibly small, number of degrees of freedom has produced the chaos (meaning that the system is deterministic). Our understanding of deterministic systems was greatly enhanced when Lorenz (1963) discovered that a simple system with as few as three differential equations can generate totally irregular fluctuations of the system’s variables — a phenomenon nowadays generally referred to as deterministic chaos. The prominent features of chaos are unpredictability over extended time periods, and sensitive dependence on initial conditions. Once started with specific initial values, the system’s future might be totally different from what it would have been if it had been started under slightly different initial conditions. Chaos may not be the ultimate description for a system’s irregular dynamic. As outlined by Rössler (1983), more complex structures “beyond chaos” may await discovery.
Originally published in Başar E, Bullock TH (eds) Brain dynamics. Springer, Berlin Heidelberg New York, pp 174-191 (Springer series in brain dynamics, vol 2). Cross references refer to that volume.
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Graf, K.E., Elbert, T. (1990). Dimensional Analysis of the Waking EEG. In: Başar, E. (eds) Chaos in Brain Function. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75545-3_11
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DOI: https://doi.org/10.1007/978-3-642-75545-3_11
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