We studied the dynamics of the sea surface temperature (SST) anomaly using a model of the temporal patterns of two sub-regions, mimicking behaviour similar to El Niño Southern Oscillations (ENSO). Specifically, we present the existence, stability, and basins of attraction of the solutions arising in the model system in the space of these parameters: self-delay, delay and inter-region coupling strengths. The emergence or suppression of oscillations in our models is a dynamical feature of utmost relevance, as it signals the presence or absence of ENSO-like oscillations. In contrast to the well-known low-order model of ENSO, where the influence of the neighbouring regions on the region of interest is modelled as external noise, we considered neighbouring regions as a coupled deterministic dynamical systems. Different parameters yielded a rich variety of dynamical patterns in our model, ranging from steady states and homogeneous oscillations to irregular oscillations and coexistence of oscillatory attractors, without explicit inclusion of noise. Interestingly, if we take the self-delay coupling strengths of the two sub-regions to be such that 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, both systems show oscillations. This implies that oscillations may arise in certain sub-regions through coupling to neighbouring regions. Namely, a sub-region with very low delay, which would naturally go to a steady state when uncoupled, yields oscillations when coupled to another sub-region with high enough delay. We explicitly obtained the basins of attraction for the different steady states and oscillatory states in the model. Our result might be helpful for forecasting of El Niño (or La Niña) progress, as it indicates the combination of initial SST anomalies in the sub-regions that can result in a El Niño/La Niña episodes. In particular, the result suggests using an interval as a criterion to estimate the El Niño or La Niño progress instead of the currently used the single value criterion.

PACS Nos 92.10.-c; 05.45.-a