Technically, the nonlinear interaction of the El Nino cycle (together with more global oceanic patterns known as ENSO) with the seasonal cycle becomes organized around the mathematical structure known as the Devil's Staircase with locked steps known as Arn'ld Tongues, a phenomena of frequency-locking according to a sequence of rational fractions, a phenomena studied by the great Russian mathematicians A.Kolmogorov and his student V. Arn'ld; see Appendix B, Figure 1:

Several things can happen as the result of this frequency-locking: the motion can be quasiperiodic with two incommensurable frequencies, the inherent El Nino frequency and its annual modulation; the motion can be irregular; or the El Nino cycle can be entrained nonlinearly into synchrony with the annual cycle for a periodic oscillation with a longer period, a subharmonic oscillation.

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