Stability and Bifurcation Analysis of Fifth-Order Nonlinear Fractional Difference Equation
In this paper, a rational difference equation with positive parameters and non-negative conditions is used to determine the presence and direction of the Neimark–Sacker bifurcation. The neimark–Sacker bifurcation of the system is first studied using the characteristic equation. In addition, we study...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/7/2/113 |
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| author | Abdul Khaliq Irfan Mustafa Tarek F. Ibrahim Waleed M. Osman Bushra R. Al-Sinan Arafa Abdalrhim Dawood Manal Yagoub Juma |
| author_facet | Abdul Khaliq Irfan Mustafa Tarek F. Ibrahim Waleed M. Osman Bushra R. Al-Sinan Arafa Abdalrhim Dawood Manal Yagoub Juma |
| author_sort | Abdul Khaliq |
| collection | DOAJ |
| description | In this paper, a rational difference equation with positive parameters and non-negative conditions is used to determine the presence and direction of the Neimark–Sacker bifurcation. The neimark–Sacker bifurcation of the system is first studied using the characteristic equation. In addition, we study bifurcation invariant curves from the perspective of normal form theory. A computer simulation is used to illustrate the analytical results. |
| first_indexed | 2024-03-11T08:48:58Z |
| format | Article |
| id | doaj.art-8966881f5a5b43b793341f1f5fcc6dbe |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T08:48:58Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-8966881f5a5b43b793341f1f5fcc6dbe2023-11-16T20:36:11ZengMDPI AGFractal and Fractional2504-31102023-01-017211310.3390/fractalfract7020113Stability and Bifurcation Analysis of Fifth-Order Nonlinear Fractional Difference EquationAbdul Khaliq0Irfan Mustafa1Tarek F. Ibrahim2Waleed M. Osman3Bushra R. Al-Sinan4Arafa Abdalrhim Dawood5Manal Yagoub Juma6Department of Mathematics, Lahore Campus, Riphah International University, Punjab 54000, PakistanDepartment of Mathematics, Lahore Campus, Riphah International University, Punjab 54000, PakistanDepartment of Mathematics, Faculty of Sciences and Arts (Mahayel), King Khalid University, Abha 62529, Saudi ArabiaDepartment of Mathematics, Faculty of Science and Arts, King Khalid University, Abha 62529, Saudi ArabiaDepartment of Administrative and Financial Sciences, Nairiyah College, University of Hafr Al-Batin, Hafr Al-Batin 31991, Saudi ArabiaDepartment of Mathematics, Faculty of Sciences and Arts in Sarat Abeda, King Khalid University, Abha 62529, Saudi ArabiaDepartment of Mathematics, Faculty of Sciences, University of Quassim, Buraidaf 52571, Saudi ArabiaIn this paper, a rational difference equation with positive parameters and non-negative conditions is used to determine the presence and direction of the Neimark–Sacker bifurcation. The neimark–Sacker bifurcation of the system is first studied using the characteristic equation. In addition, we study bifurcation invariant curves from the perspective of normal form theory. A computer simulation is used to illustrate the analytical results.https://www.mdpi.com/2504-3110/7/2/113difference equationstabilityfixed pointsNeimark–Sacker bifurcationphase portraits |
| spellingShingle | Abdul Khaliq Irfan Mustafa Tarek F. Ibrahim Waleed M. Osman Bushra R. Al-Sinan Arafa Abdalrhim Dawood Manal Yagoub Juma Stability and Bifurcation Analysis of Fifth-Order Nonlinear Fractional Difference Equation Fractal and Fractional difference equation stability fixed points Neimark–Sacker bifurcation phase portraits |
| title | Stability and Bifurcation Analysis of Fifth-Order Nonlinear Fractional Difference Equation |
| title_full | Stability and Bifurcation Analysis of Fifth-Order Nonlinear Fractional Difference Equation |
| title_fullStr | Stability and Bifurcation Analysis of Fifth-Order Nonlinear Fractional Difference Equation |
| title_full_unstemmed | Stability and Bifurcation Analysis of Fifth-Order Nonlinear Fractional Difference Equation |
| title_short | Stability and Bifurcation Analysis of Fifth-Order Nonlinear Fractional Difference Equation |
| title_sort | stability and bifurcation analysis of fifth order nonlinear fractional difference equation |
| topic | difference equation stability fixed points Neimark–Sacker bifurcation phase portraits |
| url | https://www.mdpi.com/2504-3110/7/2/113 |
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