时滞反馈作用下ENSO充电振子模型的分岔分析  

Bifurcation Analysis of the ENSO Recharge Oscillator With Time-Delayed Feedback

作　　者：刘宇丹 杜智远 赵强[1] LIU Yudan;DU Zhiyuan;ZHAO Qiang(Department of Atmospheric and Oceanic Sciences,School of Physics,Peking University,Beijing 100871,P.R.China)

机构地区：[1]北京大学物理学院大气与海洋科学系,北京100871

出　　处：《应用数学和力学》2018年第10期1128-1136,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(41175052)~~

摘　　要：通过数学变换将一类含有时滞反馈机制的ENSO充电振子模型转换成时滞Van der PolDuffing方程,并以此为基础来研究该ENSO系统的零解稳定性、Hopf分岔和极限环等动力学特征.用平均法分析了其零解的稳定性与时滞效应的强度,其和时间都有关系,讨论了时滞负反馈对ENSO振荡的影响并通过简单数值模拟验证理论分析的结果.The time-delayed impact on a class of nonlinear ENSO recharge oscillator models was investigated through transformation of the model equations into the Van der Pol-Duffing oscillator with time-delayed feedback. The Hopf bifurcation and stable limit cycles were obtained with the averaging method.Qualitative analysis shows that equilibrium stability of the ENSO system and its oscillation are closely related to the delayed feedback amplitude and time. Finally,numerical simulations were carried out to illustrate the analytical results.

关 键 词：ENSO 时滞Van der Pol-Duffing方程 HOPF分岔 

分 类 号：P433[天文地球—大气科学及气象学]