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Chaos in Vallis’ asymmetric Lorenz model for El Niño

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  • Garay, B.M.
  • Indig, B.

Abstract

We consider Vallis’ symmetric and asymmetric Lorenz models for El Niño—systems of autonomous ordinary differential equations in 3D—with the usual parameters and, in both cases, by using rigorous numerics, we locate topological horseshoes in iterates of Poincaré return maps. The computer-assisted proofs follow the standard Mischaikow–Mrozek–Zgliczynski approach. The novelty is a dimension reduction method, a direct exploitation of numerical Lorenz-like maps associated to the two components of the Poincaré section.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:75:y:2015:i:c:p:253-262
    DOI: 10.1016/j.chaos.2015.02.015
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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. II. Energy-conserving horizontal mode truncations," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 747-756.
    2. Letellier, Christophe & Roulin, Elise & Rössler, Otto E., 2006. "Inequivalent topologies of chaos in simple equations," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 337-360.
    3. 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.
    4. 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.
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    Cited by:

    1. Borghezan, Monik & Rech, Paulo C., 2017. "Chaos and periodicity in Vallis model for El Niño," Chaos, Solitons & Fractals, Elsevier, vol. 97(C), pages 15-18.

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