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Investigating chaos by the generalized alignment index town (GALI) method
One of the fundamental tasks in the study of dynamical systems is the discrimination between regular and chaotic behavior. Over the years several methods of chaos detection have been developed. Some of them, such as the construction of the system's Poincar´e Surface of Section, are appropriate for l...
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| Format: | Thesis |
| Language: | English |
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Department of Maths and Applied Maths
2020
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| _version_ | 1867613160875229184 |
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| access_status_str | Open Access |
| author | Moges, Henok Tenaw |
| author2 | Skokos, Charalampos |
| author_browse | Moges, Henok Tenaw Skokos, Charalampos |
| author_facet | Skokos, Charalampos Moges, Henok Tenaw |
| author_sort | Moges, Henok Tenaw |
| collection | Thesis |
| description | One of the fundamental tasks in the study of dynamical systems is the discrimination between regular and chaotic behavior. Over the years several methods of chaos detection have been developed. Some of them, such as the construction of the system's Poincar´e Surface of Section, are appropriate for low-dimensional systems. However, an enormous number of real-world problems are described by high-dimensional systems. Thus, modern numerical methods like the Smaller (SALI) and the Generalized (GALI) Alignment Index, which can also be used for lower-dimensional systems, are appropriate for investigating regular and chaotic motion in high-dimensional systems. In this work, we numerically investigate the behavior of the GALIs in the neighborhood of simple stable periodic orbits of the well-known Fermi-Pasta-Ulam-Tsingou lattice model. In particular, we study how the values of the GALIs depend on the width of the stability island and the system's energy. We find that the asymptotic GALI values increase when the studied regular orbits move closer to the edge of the stability island for fixed energy, while these indices decrease as the system's energy increases. We also investigate the dependence of the GALIs on the initial distribution of the coordinates of the deviation vectors used for their computation and the corresponding angles between these vectors. In this case, we show that the final constant values of the GALIs are independent of the choice of the initial deviation vectors needed for their computation. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/32284 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:31:43.046Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2020 |
| publishDateRange | 2020 |
| publishDateSort | 2020 |
| publisher | Department of Maths and Applied Maths |
| publisherStr | Department of Maths and Applied Maths |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/32284 Investigating chaos by the generalized alignment index town (GALI) method Moges, Henok Tenaw Skokos, Charalampos Mathematics One of the fundamental tasks in the study of dynamical systems is the discrimination between regular and chaotic behavior. Over the years several methods of chaos detection have been developed. Some of them, such as the construction of the system's Poincar´e Surface of Section, are appropriate for low-dimensional systems. However, an enormous number of real-world problems are described by high-dimensional systems. Thus, modern numerical methods like the Smaller (SALI) and the Generalized (GALI) Alignment Index, which can also be used for lower-dimensional systems, are appropriate for investigating regular and chaotic motion in high-dimensional systems. In this work, we numerically investigate the behavior of the GALIs in the neighborhood of simple stable periodic orbits of the well-known Fermi-Pasta-Ulam-Tsingou lattice model. In particular, we study how the values of the GALIs depend on the width of the stability island and the system's energy. We find that the asymptotic GALI values increase when the studied regular orbits move closer to the edge of the stability island for fixed energy, while these indices decrease as the system's energy increases. We also investigate the dependence of the GALIs on the initial distribution of the coordinates of the deviation vectors used for their computation and the corresponding angles between these vectors. In this case, we show that the final constant values of the GALIs are independent of the choice of the initial deviation vectors needed for their computation. 2020-09-25T07:43:13Z 2020-09-25T07:43:13Z 2020 2020-09-25T07:42:16Z Master Thesis Masters MSc http://hdl.handle.net/11427/32284 eng application/pdf Department of Maths and Applied Maths Faculty of Science |
| spellingShingle | Mathematics Moges, Henok Tenaw Investigating chaos by the generalized alignment index town (GALI) method |
| thesis_degree_str | Master's |
| title | Investigating chaos by the generalized alignment index town (GALI) method |
| title_full | Investigating chaos by the generalized alignment index town (GALI) method |
| title_fullStr | Investigating chaos by the generalized alignment index town (GALI) method |
| title_full_unstemmed | Investigating chaos by the generalized alignment index town (GALI) method |
| title_short | Investigating chaos by the generalized alignment index town (GALI) method |
| title_sort | investigating chaos by the generalized alignment index town gali method |
| topic | Mathematics |
| url | http://hdl.handle.net/11427/32284 |
| work_keys_str_mv | AT mogeshenoktenaw investigatingchaosbythegeneralizedalignmentindextowngalimethod |