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A recurrence analysis of chaotic and non-chaotic solutions within a generalized nine-dimensional Lorenz model

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  • Reyes, Tiffany
  • Shen, Bo-Wen

Abstract

Based on recent studies using high-dimensional Lorenz models (LMs), a revised view on the nature of weather has been proposed as follows: the entirety of weather is a superset that consists of both chaotic and non-chaotic processes. We suggest that better predictability may be obtained for non-chaotic processes if they can be identified in advance. In this study, to achieve the goal, we generate recurrence plots (RPs) for classifying various types of solutions obtained using simplified and full versions of the generalized Lorenz model (GLM) with various M modes, including M=3,5,7, and 9. We first perform recurrence analyses of the following solutions: (1) a periodic solution and quasi-periodic solutions containing multiple incommensurate frequencies; (2) a temporal transition from an unstable solution to a limit cycle solution, which is an isolated closed orbit; and (3) the coexistence of two types of solutions such as a steady-state and a chaotic solution or a steady-state and limit cycle solution. Various types of solutions that coexist depend only on the initial conditions (ICs).

Suggested Citation

  • Reyes, Tiffany & Shen, Bo-Wen, 2019. "A recurrence analysis of chaotic and non-chaotic solutions within a generalized nine-dimensional Lorenz model," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 1-12.
    • Handle: RePEc:eee:chsofr:v:125:y:2019:i:c:p:1-12
    DOI: 10.1016/j.chaos.2019.05.003
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    References listed on IDEAS

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    1. Roy, D. & Musielak, Z.E., 2007. "Generalized Lorenz models and their routes to chaos. I. Energy-conserving vertical mode truncations," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1038-1052.
    2. Roy, D. & Musielak, Z.E., 2007. "Generalized Lorenz models and their routes to chaos. III. Energy-conserving horizontal and vertical mode truncations," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 1064-1070.
    3. Roy, D. & Musielak, Z.E., 2007. "Generalized Lorenz models and their routes to chaos. II. Energy-conserving horizontal mode truncations," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 747-756.
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    Cited by:

    1. Cui, Jialin & Shen, Bo-Wen, 2021. "A kernel principal component analysis of coexisting attractors within a generalized Lorenz model," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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