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VNODE-LP extension for ''Chaos in Vallis’ asymmetric Lorenz model El Niño''

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VNODE-LP extension for
''Chaos in Vallis’ asymmetric Lorenz model El Niño''

B.M. Garay, B. Indig: Chaos in Vallis’ asymmetric Lorenz model for El Niño
In: 'Chaos, Solitons & Fractals' Volume 75, June 2015, Pages 253–262, ISSN 0960-0779,

Link to the paper (Open Access): http://www.sciencedirect.com/science/article/pii/S0960077915000594

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.

Supplementary material

VNODE-LP extension for ''Chaos in Vallis’ asymmetric Lorenz model El Niño''

chaos_GSL.cc: Using the GNU Scientific Library (not included) only for rapid testing purposes.

chaos_P00.cc: Using VNODE-LP (not included) for the actual computer-assisted proof in the p=0.0 z=0.3 case.

chaos_P83.cc: Using VNODE-LP (not included) for the actual computer-assisted proof in the p=0.83 z=0.3 case.

chaos_P00_Z0.3995.cc: Using VNODE-LP (not included) for the actual computer-assisted proof in the p=0.00 z=0.3995 case.

For documentation see the comments in the source files above.

License

The sources are made available under the GNU General Public License v3.0.
The paper is under the Creative Commons BY-NC-ND 4.0 License http://creativecommons.org/licenses/by-nc-nd/4.0/

VNODE-LP and other third-party tools have their own licenses. (See the paper for citations.)

Reference

If you use the sources, please cite the following paper:

B.M. Garay, B. Indig, Chaos in Vallis’ asymmetric Lorenz model for El Niño, Chaos, Solitons & Fractals, Volume 75, June 2015, Pages 253-262, ISSN 0960-0779, http://dx.doi.org/10.1016/j.chaos.2015.02.015. (http://www.sciencedirect.com/science/article/pii/S0960077915000594)

@article{Garay2015253,
title = "Chaos in Vallis’ asymmetric Lorenz model for El Niño ",
journal = "Chaos, Solitons & Fractals ",
volume = "75",
number = "0",
pages = "253 - 262",
year = "2015",
note = "",
issn = "0960-0779",
doi = "http://dx.doi.org/10.1016/j.chaos.2015.02.015",
url = "http://www.sciencedirect.com/science/article/pii/S0960077915000594",
author = "B.M. Garay and B. Indig",
abstract = "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. "
}

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