厄尔尼诺-南方波涛动时滞海气振子耦合模型的分岔分析

Bifurcation analysis for a delayed sea-air oscillator coupling model for the ENSO

本文研究了一类具有时滞的厄尔尼诺-南方波涛动模型.得到了该模型在平衡点稳定的充分条件.通过选择时滞η为分岔参数,得到了当时滞η通过一系列的临界值时,Hopf分岔产生,然后,应用中心流形和规范型理论,得到了确定Hopf分岔特性(例如Hopf分岔方向和分岔周期解的稳定性以及Hopf分岔周期解的周期等)的计算公式.最后进行数值模拟验证了所得结果的正确性.

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 7/as a bifurcation parameter, we show that Hopf bifurcation can occur when delay 7/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.