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We investigate a low-dimensional slow-fast model to understand the dynamicalorigin of El Ni\~no-Southern Oscillation. A close inspection of the systemdynamics using several bifurcation plots reveals that a sudden large expansionof the attractor occurs at a critical system parameter via a type of interiorcrisis. This interior crisis evolves through merging of a cascade ofperiod-doubling and period-adding bifurcations that leads to the origin ofoccasional amplitude-modulated extremely large events. More categorically, asituation similar to homoclinic chaos arises near the critical point, however,atypical global instability evolves as a channel-like structure in phase spaceof the system that modulates variability of amplitude and return time of theoccasional large events and makes a difference from the homoclinic chaos. Theslow-fast timescale of the low-dimensional model plays an important role on theonset of occasional extremely large events. Such extreme events arecharacterized by their heights when they exceed a threshold level measured by amean-excess function. The probability density of events' height displaysmultimodal distribution with an upper-bounded tail. We identify the dependencestructure of interevent intervals to understand the predictability of returntime of such extreme events using autoregressive integrated moving averagemodel and box plot analysis.

Understanding the origin of extreme events in El Ni\~{n}o-Southern Oscillation