Open AccessBifurcation analysis for a delayed sea-air oscillator coupling model for the ENSO
Author(s) -
Xu Chang-Jin
Publication year - 2012
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.61.220203
Subject(s) - hopf bifurcation , center manifold , transcritical bifurcation , pitchfork bifurcation , period doubling bifurcation , bifurcation diagram , coupling (piping) , bifurcation , stability (learning theory) , mathematical analysis , mathematics , physics , saddle node bifurcation , homoclinic bifurcation , nonlinear system , quantum mechanics , computer science , materials science , machine learning , metallurgy
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.