Phase portraits and orbit wise dynamics solutions, quasi-periodic and chaotic behavior of heisenberg ferromagnetic spin chains mode
This work addresses the Heisenberg ferromagnetic spin chain model through a dynamical system framework. We explore the model's phase plane by transforming it into a dynamical system, yielding diverse phase portraits based on parametric conditions. On the basis of parametric conditions and phase...
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| Language: | English |
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Elsevier
2025-03-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124004303 |
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| author | Harun-Or-Roshid Alrazi Abdeljabbar Md․ Sabur Uddin Mst․ Shekha Khatun |
| author_facet | Harun-Or-Roshid Alrazi Abdeljabbar Md․ Sabur Uddin Mst․ Shekha Khatun |
| author_sort | Harun-Or-Roshid |
| collection | DOAJ |
| description | This work addresses the Heisenberg ferromagnetic spin chain model through a dynamical system framework. We explore the model's phase plane by transforming it into a dynamical system, yielding diverse phase portraits based on parametric conditions. On the basis of parametric conditions and phase diagrams, we construct four propositions for diverse solutions along all orbits. We obtain exact results permitting along every orbit of the phase diagrams of the mode. This study yields exact solutions encompassing smooth periodic, dark, bright periodic, singular wave, dark bell solitary, bright bell solitary, bright-dark solitary wave, subharmonic wave, exponentially increasing wave, and exponentially decreasing wave solutions. By tracing the trajectory of each phase portrait, we obtain a range of numerical solutions utilizing the fourth-order Runge-Kutta method. Quasi-periodic and chaotic natures of the model extract for additional forcing term of the mode. We also test sensitivity due to small change in initial conditions in the solution of the mode. |
| format | Article |
| id | doaj-art-1586bbd0d3aa4993a967a504343ed7fc |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-1586bbd0d3aa4993a967a504343ed7fc2025-01-08T04:53:45ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-03-0113101044Phase portraits and orbit wise dynamics solutions, quasi-periodic and chaotic behavior of heisenberg ferromagnetic spin chains mode Harun-Or-Roshid0Alrazi Abdeljabbar1Md․ Sabur Uddin2Mst․ Shekha Khatun3Department of Mathematics, Pabna University of Science and Technology, Pabna 6600, Bangladesh; Department of Mathematics, Sunamgonj Science and Technology University, Shantiganj, Sunamganj 3000, Bangladesh; Corresponding authors.Department of Mathematics, Khalifa University, Abu Dhabi, United Arab Emirates; Corresponding authors.Department of Mathematics, Gono Bishwabidyalay, Savar, BangladeshDepartment of Mathematics, Sunamgonj Science and Technology University, Shantiganj, Sunamganj 3000, BangladeshThis work addresses the Heisenberg ferromagnetic spin chain model through a dynamical system framework. We explore the model's phase plane by transforming it into a dynamical system, yielding diverse phase portraits based on parametric conditions. On the basis of parametric conditions and phase diagrams, we construct four propositions for diverse solutions along all orbits. We obtain exact results permitting along every orbit of the phase diagrams of the mode. This study yields exact solutions encompassing smooth periodic, dark, bright periodic, singular wave, dark bell solitary, bright bell solitary, bright-dark solitary wave, subharmonic wave, exponentially increasing wave, and exponentially decreasing wave solutions. By tracing the trajectory of each phase portrait, we obtain a range of numerical solutions utilizing the fourth-order Runge-Kutta method. Quasi-periodic and chaotic natures of the model extract for additional forcing term of the mode. We also test sensitivity due to small change in initial conditions in the solution of the mode.http://www.sciencedirect.com/science/article/pii/S2666818124004303Heisenberg ferromagnetic spin chains modelDynamical systemChaotic behaviorSensitivity analysisBell soliton |
| spellingShingle | Harun-Or-Roshid Alrazi Abdeljabbar Md․ Sabur Uddin Mst․ Shekha Khatun Phase portraits and orbit wise dynamics solutions, quasi-periodic and chaotic behavior of heisenberg ferromagnetic spin chains mode Partial Differential Equations in Applied Mathematics Heisenberg ferromagnetic spin chains model Dynamical system Chaotic behavior Sensitivity analysis Bell soliton |
| title | Phase portraits and orbit wise dynamics solutions, quasi-periodic and chaotic behavior of heisenberg ferromagnetic spin chains mode |
| title_full | Phase portraits and orbit wise dynamics solutions, quasi-periodic and chaotic behavior of heisenberg ferromagnetic spin chains mode |
| title_fullStr | Phase portraits and orbit wise dynamics solutions, quasi-periodic and chaotic behavior of heisenberg ferromagnetic spin chains mode |
| title_full_unstemmed | Phase portraits and orbit wise dynamics solutions, quasi-periodic and chaotic behavior of heisenberg ferromagnetic spin chains mode |
| title_short | Phase portraits and orbit wise dynamics solutions, quasi-periodic and chaotic behavior of heisenberg ferromagnetic spin chains mode |
| title_sort | phase portraits and orbit wise dynamics solutions quasi periodic and chaotic behavior of heisenberg ferromagnetic spin chains mode |
| topic | Heisenberg ferromagnetic spin chains model Dynamical system Chaotic behavior Sensitivity analysis Bell soliton |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124004303 |
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