发电机
同宿轨道
单极电动机
吸引子
混乱的
物理
多稳态
经典力学
数学分析
统计物理学
数学
分叉
磁场
计算机科学
非线性系统
量子力学
人工智能
磁铁
作者
Zhouchao Wei,Irene M. Moroz,Julien Clinton Sprott,Zhen Wang,Wei Zhang
标识
DOI:10.1142/s0218127417300087
摘要
In 1979, Moffatt pointed out that the conventional treatment of the simplest self-exciting homopolar disc dynamo has inconsistencies because of the neglect of induced azimuthal eddy currents, which can be resolved by introducing a segmented disc dynamo. Here we return to the simple dynamo system proposed by Moffatt, and demonstrate previously unknown hidden chaotic attractors. Then we study multistability and coexistence of three types of attractors in the autonomous dynamo system in three dimensions: equilibrium points, limit cycles and hidden chaotic attractors. In addition, the existence of two homoclinic orbits is proved rigorously by the generalized Melnikov method. Finally, by using Poincaré compactification of polynomial vector fields in three dimensions, the dynamics near infinity of singularities is obtained.
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