一类地磁逆转模型中的Hopf分岔分析

Hopf bifurcation analysis in a geomagnetic reversal model

基于一个地磁逆转的混沌模型,我们考虑了余维一的Hopf分岔的存在性问题,通过使用李雅普诺夫稳定性理论,证明了此模型在Hopf分岔临界点附近能产生不稳定的极限环.该研究结果可以帮助我们更好理解地球磁场的逆转问题,以及平衡点的稳定性与混沌吸引子之间的关系.

Based on a chaotic model of geomagnetic reversal,we consider the existence of codimension-one Hopf bifurcation.By using Lyapunov stability theory,it is proved that this model can generate unstable limit cycles near the critical point of Hopf bifurcation.The results of this study can help us better understand the reversal problem of the Earth’s magnetic field,and the relationship between the stability of the equilibrium point and the chaotic attractor.