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Generalized Lorenz models and their routes to chaos. III. Energy-conserving horizontal and vertical mode truncations

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  • Roy, D.
  • Musielak, Z.E.

Abstract

To construct generalized Lorenz systems, higher-order modes in doubled Fourier expansions of a stream function and temperature variations must be considered. Selection of these modes is guided by the requirements that they conserve energy in the dissipationless limit and lead to systems that have bounded solutions. The previous study showed how to select the modes by using either vertical or horizontal mode truncations. In this paper, the most general method of horizontal and vertical mode truncations is presented and it is shown that the lowest-order generalized Lorenz system derived by this method is an eight dimensional system. An interesting result is that a route to chaos in this system is different than that observed in the original Lorenz model. Possible physical consequences of this result are discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:3:p:1064-1070
    DOI: 10.1016/j.chaos.2006.05.084
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    Cited by:

    1. 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.
    2. 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.
    3. 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).
    4. 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.
    5. 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.
    6. 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).

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