Bifurcation analysis for a delayed sea-air oscillator coupling model for the ENSO
- 1. Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550004, China
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Project supported by the National Natural Science Foundation of China (Grant No. 11261010), the Soft Science and Technology Program of Guizhou Province(Grant No. 2011LKC2030), the Natural Science and Technology Foundation of Guizhou Province(Grant No. J2100), the Governor Foundation of Guizhou Province (2012), and the Doctoral Foundation of Guizhou University of Finance and Economics (2010).
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.