IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v146y2021ics0960077921002186.html
   My bibliography  Save this article

A kernel principal component analysis of coexisting attractors within a generalized Lorenz model

Author

Listed:
  • Cui, Jialin
  • Shen, Bo-Wen

Abstract

Based on recent studies that reveal the coexistence of chaotic and non-chaotic solutions using a generalized Lorenz model (GLM), a revised view on the dual nature of weather has been proposed by Shen et al. [41,42], as follows: the entirety of weather is a superset consisting of both chaotic and non-chaotic processes. Since better predictability for non-chaotic processes can be expected, an effective detection of regular or chaotic solutions can improve our confidence in numerical weather and climate predictions. In this study, by performing a kernel principal component analysis of coexisting attractors obtained from the GLM, we illustrate that the time evolution of the first eigenvector of the kernel matrix, referred to as the first kernel principal component (K-PC), is effective for the classification of chaotic and non-chaotic orbits. The spatial distribution of the first K-PC within a two-dimensional phase space can depict the shape of a decision boundary that separates the chaotic and non-chaotic orbits. We additionally present how a large number (e.g., 128 or 256) of K-PCs can be used for the reconstruction of data in order to illustrate the different portions of the phase space occupied by chaotic and non-chaotic orbits, respectively.

Suggested Citation

  • 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).
  • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002186
    DOI: 10.1016/j.chaos.2021.110865
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921002186
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2021.110865?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. 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.
    4. 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.
    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. Khadija Attouri & Majdi Mansouri & Mansour Hajji & Abdelmalek Kouadri & Kais Bouzrara & Hazem Nounou, 2023. "Wind Power Converter Fault Diagnosis Using Reduced Kernel PCA-Based BiLSTM," Sustainability, MDPI, vol. 15(4), pages 1-19, February.
    2. Ziqi Yuan & Guozhu Jia, 2022. "Systematic investigation of keywords selection and processing strategy on search engine forecasting: a case of tourist volume in Beijing," Information Technology & Tourism, Springer, vol. 24(4), pages 547-580, December.
    3. Wang, Yan & Cheng, Wei & Feng, Junbo & Zang, Shengyin & Cheng, Hao & Peng, Zheng & Ren, Xiaodong & Shuai, Yubei & Liu, Hao & Pu, Xun & Yang, Junbo & Wu, Jiagui, 2022. "Silicon photonic secure communication using artificial neural network," Chaos, Solitons & Fractals, Elsevier, vol. 163(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. 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.
    2. 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).
    3. 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.
    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:146:y:2021:i:c:s0960077921002186. 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.