Chaos in Vallis' asymmetric Lorenz model for El Nino

Abstract We consider Vallis’ symmetric and asymmetric Lorenz models for El Nino—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 Poincare 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 Poincare section.

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