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We study the dynamics of the sea surface temperature (SST) anomaly using amodel of the temporal patterns of two sub-regions, mimicking behaviour similarto El Ni\~no Southern Oscillations (ENSO). Specifically, we present theexistence, stability, and basins of attraction of the solutions arising in themodel system in the space of these parameters: self delay, delay andinter-region coupling strengths. The emergence or suppression of oscillationsin our models is a dynamical feature of utmost relevance, as it signals thepresence or absence of ENSO-like oscillations. In contrast to the well-knownlow order model of ENSO, where the influence of the neighbouring regions on theregion of interest is modelled as external noise, we consider neighbouringregions as a coupled deterministic dynamical systems. Different parametersyield a rich variety of dynamical patterns in our model, ranging from steadystates and homogeneous oscillations to irregular oscillations and coexistenceof oscillatory attractors, without explicit inclusion of noise. Interestingly,if we take the self-delay coupling strengths of the two sub-regions to be suchthat the temperature of one region goes to a fixed point regime when uncoupled,while the other system is in the oscillatory regime, then on coupling bothsystems show oscillations. We explicitly obtain the basins of attraction forthe different steady states and oscillatory states in the model. Our resultsmight be helpful for forecasting of El Ni\~no (or La Ni\~na) progress, as itindicates the combination of initial SST anomalies in the sub-regions that canresult in a El Ni\~no/La Ni\~na episodes. In particular, the result suggestsusing an interval as a criterion to estimate the El-Ni\~no or La-Ni\~naprogress instead of the currently used the single value criterion.

Coexistence of attractors in a coupled nonlinear delayed system modelling El Ni\~no Southern Oscillations