Abstract
Based on the theory of information entropy concerning nonlinear errors, the growth rules for the nonlinear errors of the Lorenz system and its predictable components are studied. The results show that the impact of the uncertainties, both in the initial error and in the system itself, needs to be considered in a quantitative estimation of the system predictability. The nonlinear error growth is related to the magnitude of the initial error, and to the spatial distribution of the initial error vectors. Even if these initial errors have the same magnitude but different directions, there are also differences in the nonlinear error growth. The predictability of nonlinear error growth is related to the error component, but not related to the ratio of these components. The component with the highest/lowest rate of contribution does not necessarily have the greatest/least predictability. The different components have different predictabilities, and in different time periods, the different predictable components also have different predictabilities.
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Acknowledgements
The author gratefully thanks the two anonymous reviewers for their valuable comments. This work was supported by the National Natural Science Foundation of China (Grant No. 41375063).
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Li, A., Zhang, L., Li, X. et al. Predictable component analysis of a system based on nonlinear error information entropy. Sci. China Earth Sci. 60, 501–507 (2017). https://doi.org/10.1007/s11430-016-5127-8
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DOI: https://doi.org/10.1007/s11430-016-5127-8