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We consider a highly idealized model for El Nino/Southern Oscillation (ENSO)variability, as introduced in an earlier paper. The model is governed by adelay differential equation for sea surface temperature in the TropicalPacific, and it combines two key mechanisms that participate in ENSO dynamics:delayed negative feedback and seasonal forcing. We perform a theoretical andnumerical study of the model in the three-dimensional space of its physicallyrelevant parameters: propagation period of oceanic waves across the TropicalPacific, atmosphere-ocean coupling, and strength of seasonal forcing. Phaselocking of model solutions to the periodic forcing is prevalent: the localmaxima and minima of the solutions tend to occur at the same position withinthe seasonal cycle. Such phase locking is a key feature of the observed El Nino(warm) and La Nina (cold) events. The phasing of the extrema within theseasonal cycle depends sensitively on model parameters when forcing is weak. Wealso study co-existence of multiple solutions for fixed model parameters anddescribe the basins of attraction of the stable solutions in a one-dimensionalspace of constant initial model histories.

A delay differential model of ENSO variability, Part 2: Phase locking, multiple solutions, and dynamics of extrema