CRM CAMP in Nonlinear Analysis

Computer-Assisted Mathematical Proofs in Nonlinear Analysis

March 16, 2021 from 9:00 to 10:00 (Montreal/EST time) Zoom meeting

Computer assisted existence proof of complicated dynamics in forced delay action oscillator modelling El Nino phenomena

Seminar presented by Shin'ichi Oishi (Waseda University, Japan)

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 Nino. 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.