Hopf Bifurcation of Three-Dimensional Quadratic Jerk System
This paper is devoted to investigating the Hopf bifurcation of a three-dimensional quadratic jerk system. The stability of the singular points, the appearance of the Hopf bifurcation and the limit cycles of the system are studied. Additionally, the Liapunov quantities technique is used to study the...
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University of Baghdad, College of Science for Women
2024-07-01
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| Series: | مجلة بغداد للعلوم |
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| Online Access: | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/8945 |
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| author | Tahsin I. Rasul Rizgar H. Salih |
| author_facet | Tahsin I. Rasul Rizgar H. Salih |
| author_sort | Tahsin I. Rasul |
| collection | DOAJ |
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This paper is devoted to investigating the Hopf bifurcation of a three-dimensional quadratic jerk system. The stability of the singular points, the appearance of the Hopf bifurcation and the limit cycles of the system are studied. Additionally, the Liapunov quantities technique is used to study the cyclicity of the system and find how many limit cycles can be bifurcated from the Hopf points. Due to the computational load required for computing Liapunov quantities, some parameters are fixed. Currently, the analysis shows that three limit cycles can be bifurcated from the Hopf points. The results presented in this study are verified using MAPLE program.
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| format | Article |
| id | doaj-art-148cd45b657947d892bcebf854fec870 |
| institution | Kabale University |
| issn | 2078-8665 2411-7986 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | University of Baghdad, College of Science for Women |
| record_format | Article |
| series | مجلة بغداد للعلوم |
| spelling | doaj-art-148cd45b657947d892bcebf854fec8702025-08-20T03:58:07ZengUniversity of Baghdad, College of Science for Womenمجلة بغداد للعلوم2078-86652411-79862024-07-0121710.21123/bsj.2023.8945Hopf Bifurcation of Three-Dimensional Quadratic Jerk SystemTahsin I. Rasul 0https://orcid.org/0009-0003-8882-6244Rizgar H. Salih1https://orcid.org/0000-0001-9408-8602Department of Mathematics, Faculty of Science, Soran University, Soran, Iraq. Department of Mathematics, College of Basic Education, University of Raparin, Rania, Iraq. This paper is devoted to investigating the Hopf bifurcation of a three-dimensional quadratic jerk system. The stability of the singular points, the appearance of the Hopf bifurcation and the limit cycles of the system are studied. Additionally, the Liapunov quantities technique is used to study the cyclicity of the system and find how many limit cycles can be bifurcated from the Hopf points. Due to the computational load required for computing Liapunov quantities, some parameters are fixed. Currently, the analysis shows that three limit cycles can be bifurcated from the Hopf points. The results presented in this study are verified using MAPLE program. https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/8945Hopf bifurcation, Jerk system, Limit cycle, Liapunov quantities, Stability. |
| spellingShingle | Tahsin I. Rasul Rizgar H. Salih Hopf Bifurcation of Three-Dimensional Quadratic Jerk System مجلة بغداد للعلوم Hopf bifurcation, Jerk system, Limit cycle, Liapunov quantities, Stability. |
| title | Hopf Bifurcation of Three-Dimensional Quadratic Jerk System |
| title_full | Hopf Bifurcation of Three-Dimensional Quadratic Jerk System |
| title_fullStr | Hopf Bifurcation of Three-Dimensional Quadratic Jerk System |
| title_full_unstemmed | Hopf Bifurcation of Three-Dimensional Quadratic Jerk System |
| title_short | Hopf Bifurcation of Three-Dimensional Quadratic Jerk System |
| title_sort | hopf bifurcation of three dimensional quadratic jerk system |
| topic | Hopf bifurcation, Jerk system, Limit cycle, Liapunov quantities, Stability. |
| url | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/8945 |
| work_keys_str_mv | AT tahsinirasul hopfbifurcationofthreedimensionalquadraticjerksystem AT rizgarhsalih hopfbifurcationofthreedimensionalquadraticjerksystem |