Abstract
In this paper, a delayed sea-air oscillator coupling model for the ENSO is investigated. We obtain the sufficient condition of stability in equilibrium. By choosing delay η as a bifurcation parameter, we show that Hopf bifurcation can occur when delay η passes through a sequence of critical values. Meanwhile, based on the center manifold theory and the normal form approach, we derive the formula for determining the properties of Hopf bifurcating periodic orbit, such as the direction of Hopf bifurcation, the stability of Hopf bifurcating periodic solution and the periodic of Hopf bifurcating periodic solution. Finally, numerical simulations are carried out to illustrate the analytical results.
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