Limit Cycles of Lorenz System with Hopf Bifurcation
We prove that near the bifurcation point unstable limit cycle arises from the Lorenz system. In the analysis, we use the method of local bifurcation theory, especially the center manifold and the normal form theorem. A computer algebra system using Maple to derive all the formulas and verify the res...
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| Format: | Article |
| Language: | English |
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Mosul University
2008-07-01
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| Series: | Al-Rafidain Journal of Computer Sciences and Mathematics |
| Subjects: | |
| Online Access: | https://csmj.mosuljournals.com/article_163951_1d90dd7accb190de4aa5ef95b0d89f70.pdf |
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| _version_ | 1849727745513226240 |
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| author | Azad Amen Rizgar Salih |
| author_facet | Azad Amen Rizgar Salih |
| author_sort | Azad Amen |
| collection | DOAJ |
| description | We prove that near the bifurcation point unstable limit cycle arises from the Lorenz system. In the analysis, we use the method of local bifurcation theory, especially the center manifold and the normal form theorem. A computer algebra system using Maple to derive all the formulas and verify the results presented in this paper. |
| format | Article |
| id | doaj-art-6de4a6c45f294383bbde8d38b32d156c |
| institution | DOAJ |
| issn | 1815-4816 2311-7990 |
| language | English |
| publishDate | 2008-07-01 |
| publisher | Mosul University |
| record_format | Article |
| series | Al-Rafidain Journal of Computer Sciences and Mathematics |
| spelling | doaj-art-6de4a6c45f294383bbde8d38b32d156c2025-08-20T03:09:45ZengMosul UniversityAl-Rafidain Journal of Computer Sciences and Mathematics1815-48162311-79902008-07-0151819910.33899/csmj.2008.163951163951Limit Cycles of Lorenz System with Hopf BifurcationAzad Amen0Rizgar Salih1College of Basic Education University of SalahaddinCollege of science University of SulaimaniWe prove that near the bifurcation point unstable limit cycle arises from the Lorenz system. In the analysis, we use the method of local bifurcation theory, especially the center manifold and the normal form theorem. A computer algebra system using Maple to derive all the formulas and verify the results presented in this paper.https://csmj.mosuljournals.com/article_163951_1d90dd7accb190de4aa5ef95b0d89f70.pdflorenz systemlimit cyclecenter manifold and normal formhopf bifurcation |
| spellingShingle | Azad Amen Rizgar Salih Limit Cycles of Lorenz System with Hopf Bifurcation Al-Rafidain Journal of Computer Sciences and Mathematics lorenz system limit cycle center manifold and normal form hopf bifurcation |
| title | Limit Cycles of Lorenz System with Hopf Bifurcation |
| title_full | Limit Cycles of Lorenz System with Hopf Bifurcation |
| title_fullStr | Limit Cycles of Lorenz System with Hopf Bifurcation |
| title_full_unstemmed | Limit Cycles of Lorenz System with Hopf Bifurcation |
| title_short | Limit Cycles of Lorenz System with Hopf Bifurcation |
| title_sort | limit cycles of lorenz system with hopf bifurcation |
| topic | lorenz system limit cycle center manifold and normal form hopf bifurcation |
| url | https://csmj.mosuljournals.com/article_163951_1d90dd7accb190de4aa5ef95b0d89f70.pdf |
| work_keys_str_mv | AT azadamen limitcyclesoflorenzsystemwithhopfbifurcation AT rizgarsalih limitcyclesoflorenzsystemwithhopfbifurcation |