Chaos in Vallis' asymmetric Lorenz model for El Niño

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.