Inclusion of periodic solutions for forced delay differential equation modeling El Niño

Abstract

A computer assisted proof is presented for the existence of various periodic solutions for forced Suarez-Schopf's equation, which are delay differential equations modeling El Niño. Tight inclusions of periodic solutions are calculated through numerical verification method by utilizing a structure of Galerkin's equation for forced Suarez-Schopf's equation effectively. The existence of various periodic solutions has been proved via computer assisted proofs including various subharmonics. Especially, coexistence of several subharmonics are proved and numerical simulations are presented suggesting an appearance of chaos.