Stability analysis and suppress chaos in the generalized Lorenz model
In this paper, we investigate the stability analysis of the equilibrium points and the influence of the orientation on the suppression of chaotic behavior of the generalized Lorenz system proposed. A three-dimensional system model is obtained using the spectral method. We proved that the first equil...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-06-01
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| Series: | Chaos, Solitons & Fractals: X |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590054424000010 |
| _version_ | 1797317484730122240 |
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| author | Hamza Rouah |
| author_facet | Hamza Rouah |
| author_sort | Hamza Rouah |
| collection | DOAJ |
| description | In this paper, we investigate the stability analysis of the equilibrium points and the influence of the orientation on the suppression of chaotic behavior of the generalized Lorenz system proposed. A three-dimensional system model is obtained using the spectral method. We proved that the first equilibrium point is globally asymptotically stable and the other two equilibria are asymptotically stable under certain conditions on the control parameters σ, P, r, b1 and b2. These theoretical results are supported by numerical simulations. Also, we showed that chaos can be suppressed by a boundary crisis or period-doubling by choosing an appropriate tilt angle. Bifurcation diagrams are drawn to confirm these results. |
| first_indexed | 2024-03-08T03:35:41Z |
| format | Article |
| id | doaj.art-e0bf33fbe5714d59ba0143ed4f5f9fe6 |
| institution | Directory Open Access Journal |
| issn | 2590-0544 |
| language | English |
| last_indexed | 2024-03-08T03:35:41Z |
| publishDate | 2024-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Chaos, Solitons & Fractals: X |
| spelling | doaj.art-e0bf33fbe5714d59ba0143ed4f5f9fe62024-02-10T04:45:17ZengElsevierChaos, Solitons & Fractals: X2590-05442024-06-0112100104Stability analysis and suppress chaos in the generalized Lorenz modelHamza Rouah0Department of Mathematics, FSTM, Laboratory of Mathematics and Applications, University Hassan II-Casablanca, PO Box146, Mohammedia, MoroccoIn this paper, we investigate the stability analysis of the equilibrium points and the influence of the orientation on the suppression of chaotic behavior of the generalized Lorenz system proposed. A three-dimensional system model is obtained using the spectral method. We proved that the first equilibrium point is globally asymptotically stable and the other two equilibria are asymptotically stable under certain conditions on the control parameters σ, P, r, b1 and b2. These theoretical results are supported by numerical simulations. Also, we showed that chaos can be suppressed by a boundary crisis or period-doubling by choosing an appropriate tilt angle. Bifurcation diagrams are drawn to confirm these results.http://www.sciencedirect.com/science/article/pii/S2590054424000010Stability analysisChaosFourier modesBifurcation diagram |
| spellingShingle | Hamza Rouah Stability analysis and suppress chaos in the generalized Lorenz model Chaos, Solitons & Fractals: X Stability analysis Chaos Fourier modes Bifurcation diagram |
| title | Stability analysis and suppress chaos in the generalized Lorenz model |
| title_full | Stability analysis and suppress chaos in the generalized Lorenz model |
| title_fullStr | Stability analysis and suppress chaos in the generalized Lorenz model |
| title_full_unstemmed | Stability analysis and suppress chaos in the generalized Lorenz model |
| title_short | Stability analysis and suppress chaos in the generalized Lorenz model |
| title_sort | stability analysis and suppress chaos in the generalized lorenz model |
| topic | Stability analysis Chaos Fourier modes Bifurcation diagram |
| url | http://www.sciencedirect.com/science/article/pii/S2590054424000010 |
| work_keys_str_mv | AT hamzarouah stabilityanalysisandsuppresschaosinthegeneralizedlorenzmodel |