Статья

Detecting Hidden Chaotic Regions and Complex Dynamics in the Self-Exciting Homopolar Disc Dynamo

Zhouchao WeiCollege of Mechanical Engineering, Beijing University of Technology, Beijing 100124, P. R. ChinaIrene M. MorozMathematical Institute, University of Oxford, Oxford, OX2 6GG, EnglandJ. C. SprottDepartment of Physics, University of Wisconsin, Madison, WI 53706, USAZhen WangDepartment of Applied Sciences, Xijing University, Xi’an 710123, P. R. ChinaWei ZhangCollege of Mechanical Engineering, Beijing University of Technology, Beijing 100124, P. R. China

2017en

ABI

Аннотация

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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Идентификаторы

DOI: 10.1142/s0218127417300087

Цитирования и источники

Цитирований: 2Использованных источников: 0

Показатели — AkademScholar