IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v125y2019icp1-12.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077919301602
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.05.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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).
    2. Garay, B.M. & Indig, B., 2015. "Chaos in Vallis’ asymmetric Lorenz model for El Niño," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 253-262.
    3. Khodakaram-Tafti, Amin & Emdad, Homayoun & Mahzoon, Mojtaba, 2022. "Dynamical and chaotic behaviors of natural convection flow in semi-annular cylindrical domains using energy-conserving low-order spectral models," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    4. Duan, Zhisheng & Wang, Jinzhi & Yang, Ying & Huang, Lin, 2009. "Frequency-domain and time-domain methods for feedback nonlinear systems and applications to chaos control," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 848-861.
    5. Khodakaram-Tafti, Amin & Emdad, Homayoun & Mahzoon, Mojtaba, 2024. "Periodicity and chaos of thermal convective flows in annular cylindrical domains using the method of isolation by spectral expansions," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    6. Ayati, Moosa & Khaloozadeh, Hamid, 2009. "A stable adaptive synchronization scheme for uncertain chaotic systems via observer," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2473-2483.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:125:y:2019:i:c:p:1-12. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.