Detecting hidden chaotic regions and complex dynamics in the self-exciting homopolar disc dynamo
In 1979, H. K. Moffatt has 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...
| Main Authors: | , , , , |
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| Format: | Journal article |
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World Scientific Publishing
2017
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| _version_ | 1797101345766899712 |
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| author | Moroz, I Wei, Z Sprott, J Wang, Z Zhang, W |
| author_facet | Moroz, I Wei, Z Sprott, J Wang, Z Zhang, W |
| author_sort | Moroz, I |
| collection | OXFORD |
| description | In 1979, H. K. Moffatt has 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 Poincar´e compactification of polynomial vector fields in three dimensions, the dynamics near infinity of singularities is obtained. |
| first_indexed | 2024-03-07T05:50:33Z |
| format | Journal article |
| id | oxford-uuid:e8bbf75b-1719-432f-a825-25ae9fbb3323 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:50:33Z |
| publishDate | 2017 |
| publisher | World Scientific Publishing |
| record_format | dspace |
| spelling | oxford-uuid:e8bbf75b-1719-432f-a825-25ae9fbb33232022-03-27T10:48:58ZDetecting hidden chaotic regions and complex dynamics in the self-exciting homopolar disc dynamoJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e8bbf75b-1719-432f-a825-25ae9fbb3323Symplectic Elements at OxfordWorld Scientific Publishing2017Moroz, IWei, ZSprott, JWang, ZZhang, WIn 1979, H. K. Moffatt has 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 Poincar´e compactification of polynomial vector fields in three dimensions, the dynamics near infinity of singularities is obtained. |
| spellingShingle | Moroz, I Wei, Z Sprott, J Wang, Z Zhang, W Detecting hidden chaotic regions and complex dynamics in the self-exciting homopolar disc dynamo |
| title | Detecting hidden chaotic regions and complex dynamics in the self-exciting homopolar disc dynamo |
| title_full | Detecting hidden chaotic regions and complex dynamics in the self-exciting homopolar disc dynamo |
| title_fullStr | Detecting hidden chaotic regions and complex dynamics in the self-exciting homopolar disc dynamo |
| title_full_unstemmed | Detecting hidden chaotic regions and complex dynamics in the self-exciting homopolar disc dynamo |
| title_short | Detecting hidden chaotic regions and complex dynamics in the self-exciting homopolar disc dynamo |
| title_sort | detecting hidden chaotic regions and complex dynamics in the self exciting homopolar disc dynamo |
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