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Forecasting and Chaos

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Predictability of Chaotic Dynamics

Part of the book series: Springer Series in Synergetics ((SSSYN))

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Abstract

Forecasting is the process of making predictions of the future based on past and present data. One of the key questions of the scientific method is the possibility of making predictions using a model and to confront them with new observations as a test of its goodness. It seems rather natural to think that with an adequate increase in numerical computational facilities, the errors could be neglected and that from a set of initial conditions which are known with enough precision, one could predict the future state of a dynamical system. However, every model has inherent inaccuracies leading its results to deviate from the true solution. Furthermore, the computational issues constitute another source of errors. When a system shows a strong sensitivity to the initial conditions, then the system is chaotic. And when the nonlinearity is present, one prediction can be destroyed by an initial error, even by a very small one. Fortunately, the presence of chaos does not always imply a low predictability. An orbit can be chaotic and still be predictable, in the sense that the chaotic orbit is followed, or shadowed, by a real orbit, thus making its predictions physically valid.

The original version of this chapter was revised. An erratum to this chapter can be found at DOI 10.1007/978-3-319-51893-0_5

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Notes

  1. 1.

    In 1843, the British mathematician and astronomer John Couch Adams also began to work on the orbit of Uranus using the data he had, and he has been sometimes credited by the discovery of Neptune.

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  1. Department of Physics, Universidad Rey Juan Carlos, Móstoles, Madrid, Spain

    Juan C. Vallejo & Miguel A. F. Sanjuan

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  1. Juan C. Vallejo
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  2. Miguel A. F. Sanjuan
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Vallejo, J.C., Sanjuan, M.A.F. (2017). Forecasting and Chaos. In: Predictability of Chaotic Dynamics . Springer Series in Synergetics. Springer, Cham. https://doi.org/10.1007/978-3-319-51893-0_1

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