Analysis of the multi-phenomenal nonlinear system : Testing Integrability and detecting chaos
As a large extension in Hamiltonian form, the system of a PT symmetric dimer of coupled nonlinear oscillators is developed. This system provides an explanation for a number of problems with Hamiltonian dynamics. Integrability is evaluated in the Painlevé sense of the system. The system reported twel...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-04-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379723001390 |
| _version_ | 1797852008759164928 |
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| author | Mohamed Benkhali Jaouad Kharbach Zakia Hammouch Walid Chatar Mohammed El Ghamari Abdellah Rezzouk Mohammed Ouazzani-Jamil |
| author_facet | Mohamed Benkhali Jaouad Kharbach Zakia Hammouch Walid Chatar Mohammed El Ghamari Abdellah Rezzouk Mohammed Ouazzani-Jamil |
| author_sort | Mohamed Benkhali |
| collection | DOAJ |
| description | As a large extension in Hamiltonian form, the system of a PT symmetric dimer of coupled nonlinear oscillators is developed. This system provides an explanation for a number of problems with Hamiltonian dynamics. Integrability is evaluated in the Painlevé sense of the system. The system reported twelve P-cases. First integrals of planar motion are constructed explicitly for each integrable case to show the Liouvillian integrability of the equations of motion. A mixture of numerical approaches is used to test the theoretical conclusions in order to identify the nature of orbits and evaluate the system’s transition from order to chaos. These techniques consist of the Poincaré Section Surface, the maximum Lyapunov Exponent, and the Smaller Alignment Index. |
| first_indexed | 2024-04-09T19:25:59Z |
| format | Article |
| id | doaj.art-d112b19fcbb343c98b9335e05f91d8ef |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-04-09T19:25:59Z |
| publishDate | 2023-04-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-d112b19fcbb343c98b9335e05f91d8ef2023-04-05T08:12:23ZengElsevierResults in Physics2211-37972023-04-0147106346Analysis of the multi-phenomenal nonlinear system : Testing Integrability and detecting chaosMohamed Benkhali0Jaouad Kharbach1Zakia Hammouch2Walid Chatar3Mohammed El Ghamari4Abdellah Rezzouk5Mohammed Ouazzani-Jamil6Laboratoire de Physique du Solide, Faculté des Sciences Dhar El Mahraz, Université Sidi Mohamed Ben Abdellah, B.P. 1796, 30000 Fez-Atlas, MoroccoLaboratoire de Physique du Solide, Faculté des Sciences Dhar El Mahraz, Université Sidi Mohamed Ben Abdellah, B.P. 1796, 30000 Fez-Atlas, MoroccoEcole Normale Supérieure de Meknès, Université Moulay Ismail, Morocco; Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Viet Nam; Department of Medical Research, China Medical University Hospital, Taichung, Taiwan; Université Privée de Fès, Laboratoire Systèmes et Environnements Durables, Lot. Quaraouiyine Route Ain Chkef, Fès, Morocco; Corresponding author at: Ecole Normale Supérieure de Meknès, Université Moulay Ismail, Morocco.Laboratoire de Physique du Solide, Faculté des Sciences Dhar El Mahraz, Université Sidi Mohamed Ben Abdellah, B.P. 1796, 30000 Fez-Atlas, MoroccoLaboratoire de Physique du Solide, Faculté des Sciences Dhar El Mahraz, Université Sidi Mohamed Ben Abdellah, B.P. 1796, 30000 Fez-Atlas, MoroccoLaboratoire de Physique du Solide, Faculté des Sciences Dhar El Mahraz, Université Sidi Mohamed Ben Abdellah, B.P. 1796, 30000 Fez-Atlas, MoroccoUniversité Privée de Fès, Laboratoire Systèmes et Environnements Durables, Lot. Quaraouiyine Route Ain Chkef, Fès, MoroccoAs a large extension in Hamiltonian form, the system of a PT symmetric dimer of coupled nonlinear oscillators is developed. This system provides an explanation for a number of problems with Hamiltonian dynamics. Integrability is evaluated in the Painlevé sense of the system. The system reported twelve P-cases. First integrals of planar motion are constructed explicitly for each integrable case to show the Liouvillian integrability of the equations of motion. A mixture of numerical approaches is used to test the theoretical conclusions in order to identify the nature of orbits and evaluate the system’s transition from order to chaos. These techniques consist of the Poincaré Section Surface, the maximum Lyapunov Exponent, and the Smaller Alignment Index.http://www.sciencedirect.com/science/article/pii/S2211379723001390Multi-phenomenal nonlinear systemPainlevé analysisIntegrabilityIntegrals of motionSmaller Alignment IndexPoincaré Section Surface |
| spellingShingle | Mohamed Benkhali Jaouad Kharbach Zakia Hammouch Walid Chatar Mohammed El Ghamari Abdellah Rezzouk Mohammed Ouazzani-Jamil Analysis of the multi-phenomenal nonlinear system : Testing Integrability and detecting chaos Results in Physics Multi-phenomenal nonlinear system Painlevé analysis Integrability Integrals of motion Smaller Alignment Index Poincaré Section Surface |
| title | Analysis of the multi-phenomenal nonlinear system : Testing Integrability and detecting chaos |
| title_full | Analysis of the multi-phenomenal nonlinear system : Testing Integrability and detecting chaos |
| title_fullStr | Analysis of the multi-phenomenal nonlinear system : Testing Integrability and detecting chaos |
| title_full_unstemmed | Analysis of the multi-phenomenal nonlinear system : Testing Integrability and detecting chaos |
| title_short | Analysis of the multi-phenomenal nonlinear system : Testing Integrability and detecting chaos |
| title_sort | analysis of the multi phenomenal nonlinear system testing integrability and detecting chaos |
| topic | Multi-phenomenal nonlinear system Painlevé analysis Integrability Integrals of motion Smaller Alignment Index Poincaré Section Surface |
| url | http://www.sciencedirect.com/science/article/pii/S2211379723001390 |
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