A novel approach to the convergence analysis of chaotic dynamics in fractional order Chua’s attractor model employing fixed points
This article uses a fixed point method to connect with Chua’s attractor model, incorporating the Atangana–Baleanu derivative using a two-step Lagrange polynomial. We introduce novel fixed point theorems using some special contractions followed by graphical representations of the convergence behavior...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-01-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016824011566 |
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| author | Mudasir Younis Haroon Ahmad Mahpeyker Ozturk Deepak Singh |
| author_facet | Mudasir Younis Haroon Ahmad Mahpeyker Ozturk Deepak Singh |
| author_sort | Mudasir Younis |
| collection | DOAJ |
| description | This article uses a fixed point method to connect with Chua’s attractor model, incorporating the Atangana–Baleanu derivative using a two-step Lagrange polynomial. We introduce novel fixed point theorems using some special contractions followed by graphical representations of the convergence behavior of the iterative process. The uniqueness and existence of fixed points are demonstrated through theoretical proofs and numerical simulations. This approach of its first kind substantiates the existence and uniqueness of the model, enriching the understanding of its chaotic dynamics. Furthermore, numerical investigations explore distinct scenarios of Chua’s model, encompassing the classic Chua’s attractor, the double scroll attractor, chaos in Chua’s circuit, and behaviors such as cycle behavior and higher parametric values. Each case is analyzed graphically, providing insights into the system’s complex dynamics and validating theoretical predictions. |
| format | Article |
| id | doaj-art-2e5da30cb23543a8bf5465956cb16516 |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-2e5da30cb23543a8bf5465956cb165162025-01-09T06:13:21ZengElsevierAlexandria Engineering Journal1110-01682025-01-01110363375A novel approach to the convergence analysis of chaotic dynamics in fractional order Chua’s attractor model employing fixed pointsMudasir Younis0Haroon Ahmad1Mahpeyker Ozturk2Deepak Singh3Department of Mathematics, Faculty of Science, Sakarya University, Sakarya, 54050, TurkeyAbdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, PakistanDepartment of Mathematics, Faculty of Science, Sakarya University, Sakarya, 54050, Turkey; Corresponding author.Department of Applied Sciences, National Institute of Technical Teachers’ Training and Research, Bhopal, IndiaThis article uses a fixed point method to connect with Chua’s attractor model, incorporating the Atangana–Baleanu derivative using a two-step Lagrange polynomial. We introduce novel fixed point theorems using some special contractions followed by graphical representations of the convergence behavior of the iterative process. The uniqueness and existence of fixed points are demonstrated through theoretical proofs and numerical simulations. This approach of its first kind substantiates the existence and uniqueness of the model, enriching the understanding of its chaotic dynamics. Furthermore, numerical investigations explore distinct scenarios of Chua’s model, encompassing the classic Chua’s attractor, the double scroll attractor, chaos in Chua’s circuit, and behaviors such as cycle behavior and higher parametric values. Each case is analyzed graphically, providing insights into the system’s complex dynamics and validating theoretical predictions.http://www.sciencedirect.com/science/article/pii/S1110016824011566Extended suprametric spaceCiric contractionReich contractionℱ-type contractionGupta–Saxena contractionChua’s attractors |
| spellingShingle | Mudasir Younis Haroon Ahmad Mahpeyker Ozturk Deepak Singh A novel approach to the convergence analysis of chaotic dynamics in fractional order Chua’s attractor model employing fixed points Alexandria Engineering Journal Extended suprametric space Ciric contraction Reich contraction ℱ-type contraction Gupta–Saxena contraction Chua’s attractors |
| title | A novel approach to the convergence analysis of chaotic dynamics in fractional order Chua’s attractor model employing fixed points |
| title_full | A novel approach to the convergence analysis of chaotic dynamics in fractional order Chua’s attractor model employing fixed points |
| title_fullStr | A novel approach to the convergence analysis of chaotic dynamics in fractional order Chua’s attractor model employing fixed points |
| title_full_unstemmed | A novel approach to the convergence analysis of chaotic dynamics in fractional order Chua’s attractor model employing fixed points |
| title_short | A novel approach to the convergence analysis of chaotic dynamics in fractional order Chua’s attractor model employing fixed points |
| title_sort | novel approach to the convergence analysis of chaotic dynamics in fractional order chua s attractor model employing fixed points |
| topic | Extended suprametric space Ciric contraction Reich contraction ℱ-type contraction Gupta–Saxena contraction Chua’s attractors |
| url | http://www.sciencedirect.com/science/article/pii/S1110016824011566 |
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