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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 23, issue 4
Nonlin. Processes Geophys., 23, 189–203, 2016
https://doi.org/10.5194/npg-23-189-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
Nonlin. Processes Geophys., 23, 189–203, 2016
https://doi.org/10.5194/npg-23-189-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 08 Jul 2016

Research article | 08 Jul 2016

Hierarchical scale dependence associated with the extension of the nonlinear feedback loop in a seven-dimensional Lorenz model

Bo-Wen Shen

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Cited articles

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Benettin, G., Galgani, L., Giorgilli, A., and Strelcyn, J. M.: Lyapunov Characteristic Exponents fro Smooth Dynamical Systems and for Hamiltonian Systems; A method for computing all of them. Part 1: Theory, Meccanica, 15, 9–20, 1980.
Biswas, R., Aftosmis, M. J., Kiris, C., and Shen, B.-W.: Petascale computing: Impact on future NASA missions, in: Petascale Computing: Architectures and Algorithms, edited by: Bader, D., Chapman and Hall/CRC Press, Boca Raton, FL, 29–46, 2007.
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Short summary
We construct a seven-dimensional Lorenz model (7DLM) to discuss the impact of an extended nonlinear feedback loop on solutions' stability and illustrate the hierarchical scale dependence of chaotic solutions. The 7DLM requires a much larger critical value for the Rayleigh parameter (rc ∼ 116.9) for the onset of chaos. For chaotic solutions with r = 120, high correlation coefficients among the modes at different scales indicate hierarchical scale dependence.
We construct a seven-dimensional Lorenz model (7DLM) to discuss the impact of an extended...
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