Delayed Feedback Versus Seasonal Forcing: Resonance Phenomena in an El Nin͂o Southern Oscillation Model

Climate models can take many different forms, from very detailed highly computational models with hundreds of thousands of variables, to more phenomenological models of only a few variables that are designed to investigate fundamental relationships in the climate system. Important ingredients in these models are the periodic forcing by the seasons, as well as global transport phenomena of quantities such as air or ocean temperature and salinity. We consider a phenomenological model for the El Nino Southern Oscillation system, where the delayed effects of oceanic waves are incorporated explicitly into the model. This gives a description by a delay differential equation, which models underlying fundamental processes of the interaction between internal delay-induced oscillations and the external forcing. The combination of delay and forcing in differential equations has also found application in other fields, such as ecology and gene networks. Specifically, we present exemplary stable solutions of the model...