A Fractional Recharge-Discharge Model for ENSO

抄録

The ENSO phenomenon is investigated by building a fractional derivative recharge-discharge model in which the integer derivative is replaced with the left-sided Caputo type fractional derivative. The results suggest that when the highest order fractional derivative is larger than 1 but smaller than or equal to 2, the model exhibits a variation between exponential decay and pure harmonic oscillation. The system will strengthen to an El Niño/La Niña event and then weaken to the neutral state which does not require a zero value. Therefore, there is only a life cycle of an El Niño/La Niña event, rather than the life cycle of a complete ENSO event in the pure harmonic oscillation. When the highest order fractional derivative is larger than 2, the model exhibits an exponential-like amplified oscillation. The system benefits to exhibit the life cycle of strong ENSO events. The fractional derivative recharge-discharge model, in general, extends the integer model and can be applied in studying the complexity in ENSO phenomenon.