Interannual variability in a tropical atmosphere–ocean model: Influence of the basic state, ocean geometry and nonlinearity. Berlin: Springer Science & Business Media.īattisti, D.S., and A.C. Geometrical methods in the theory of ordinary differential equations, 2nd ed., Grundlehren der mathematischen Wissenschaften, vol. It is shown that the chaos-to-chaos crisis may or may not survive the addition of small noise to the evolution equation, depending on how the noise enters the latter. The effect of noise on this phase-and-parameter space behavior is then discussed. These regions are those that exhibit robust foldings with respect to perturbations. The analysis reveals that regions of the strange PBA that survive the crisis are those populated by the most probable states of the system. The change is associated with the sudden disappearance of the most extreme warm (El Niño) and cold (La Niña) events, as one crosses the critical parameter value from below. The crisis manifests itself by a brutal change not only in the size but also in the shape of the PBA. Both chaotic regimes correspond to an overlapping of resonances but the two differ by the properties of this overlapping. Since the PBA is dominated by chaotic behavior, we refer to it as a strange PBA. The control parameter is the intensity of the positive feedback and the PBA undergoes a crisis that consists of a chaos-to-chaos transition. We study the pullback attractor (PBA) of a seasonally forced delay differential model for the El Niño–Southern Oscillation (ENSO) the model has two delays, associated with a positive and a negative feedback.
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