Chaos in Vallis' asymmetric Lorenz model for El Niño

Highlights: •Vallis' symmetric and asymmetric Lorenz models for El Niño are compared. •A computer-assisted proof for chaos (topological horseshoes) is provided. •A difference between the nature of chaos in these two models is pointed out. •The novelty is the direct exploitation of Lorenz maps on 'crescent-shaped curves'. •A brief overview of chaos in El Niño thermocline oscillation models is given. -- 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