Qualitative Analysis of a Hyperchaotic Lorenz-Stenflo Mathematical Model via the Caputo Fractional Operator
The Lorenz-Stenflo mathematical model describes a complex dynamical behavior related to atmospheric acoustic-gravity waves. In this study, qualitative analysis of the four-dimensional hyperchaotic Lorenz-Stenflo system via the Caputo fractional derivative is implemented. By using the Matignon stabil...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/4975104 |
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| author | Chernet Tuge Deressa Sina Etemad Mohammed K. A. Kaabar Shahram Rezapour |
| author_facet | Chernet Tuge Deressa Sina Etemad Mohammed K. A. Kaabar Shahram Rezapour |
| author_sort | Chernet Tuge Deressa |
| collection | DOAJ |
| description | The Lorenz-Stenflo mathematical model describes a complex dynamical behavior related to atmospheric acoustic-gravity waves. In this study, qualitative analysis of the four-dimensional hyperchaotic Lorenz-Stenflo system via the Caputo fractional derivative is implemented. By using the Matignon stability criterion, the local stability analysis of the system showed that all the equilibrium points of the system are locally unstable. Calculation of the Lyapunov exponents along with the relevant bifurcation diagrams with respect to different fractional orders exposed the hyperchaotic dynamical behavior for the system. Bifurcation diagrams for all the four parameters in the system also showed the hyperchaotic nature of the Lorenz-Stenflo system. Different phase attractors of the system corresponding to different fractional derivatives and parameters are presented to specify the dynamical nature of the system. The Lorenz-Stenflo system showed sensitivity to initial conditions. The master and slave systems showed a strong correlation among themselves, as verified by graphs of time series solutions of the two systems. |
| format | Article |
| id | doaj-art-be5a3c26717b4cc5a9f56f0025b29225 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-be5a3c26717b4cc5a9f56f0025b292252025-02-03T06:45:54ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/4975104Qualitative Analysis of a Hyperchaotic Lorenz-Stenflo Mathematical Model via the Caputo Fractional OperatorChernet Tuge Deressa0Sina Etemad1Mohammed K. A. Kaabar2Shahram Rezapour3College of Natural SciencesDepartment of MathematicsGofa CampDepartment of MathematicsThe Lorenz-Stenflo mathematical model describes a complex dynamical behavior related to atmospheric acoustic-gravity waves. In this study, qualitative analysis of the four-dimensional hyperchaotic Lorenz-Stenflo system via the Caputo fractional derivative is implemented. By using the Matignon stability criterion, the local stability analysis of the system showed that all the equilibrium points of the system are locally unstable. Calculation of the Lyapunov exponents along with the relevant bifurcation diagrams with respect to different fractional orders exposed the hyperchaotic dynamical behavior for the system. Bifurcation diagrams for all the four parameters in the system also showed the hyperchaotic nature of the Lorenz-Stenflo system. Different phase attractors of the system corresponding to different fractional derivatives and parameters are presented to specify the dynamical nature of the system. The Lorenz-Stenflo system showed sensitivity to initial conditions. The master and slave systems showed a strong correlation among themselves, as verified by graphs of time series solutions of the two systems.http://dx.doi.org/10.1155/2022/4975104 |
| spellingShingle | Chernet Tuge Deressa Sina Etemad Mohammed K. A. Kaabar Shahram Rezapour Qualitative Analysis of a Hyperchaotic Lorenz-Stenflo Mathematical Model via the Caputo Fractional Operator Journal of Function Spaces |
| title | Qualitative Analysis of a Hyperchaotic Lorenz-Stenflo Mathematical Model via the Caputo Fractional Operator |
| title_full | Qualitative Analysis of a Hyperchaotic Lorenz-Stenflo Mathematical Model via the Caputo Fractional Operator |
| title_fullStr | Qualitative Analysis of a Hyperchaotic Lorenz-Stenflo Mathematical Model via the Caputo Fractional Operator |
| title_full_unstemmed | Qualitative Analysis of a Hyperchaotic Lorenz-Stenflo Mathematical Model via the Caputo Fractional Operator |
| title_short | Qualitative Analysis of a Hyperchaotic Lorenz-Stenflo Mathematical Model via the Caputo Fractional Operator |
| title_sort | qualitative analysis of a hyperchaotic lorenz stenflo mathematical model via the caputo fractional operator |
| url | http://dx.doi.org/10.1155/2022/4975104 |
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