A New Circumscribed Self-Excited Spherical Strange Attractor
Studying new chaotic flows with specific characteristics has been an open-ended field of exploring nonlinear dynamics. Investigation of chaotic flows is an area of research that has been taken into consideration for many years; thus, it helps in a better understanding of the chaotic systems. In this...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/8068737 |
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| author | Ramesh Ramamoorthy Sajjad Shaukat Jamal Iqtadar Hussain Mahtab Mehrabbeik Sajad Jafari Karthikeyan Rajagopal |
| author_facet | Ramesh Ramamoorthy Sajjad Shaukat Jamal Iqtadar Hussain Mahtab Mehrabbeik Sajad Jafari Karthikeyan Rajagopal |
| author_sort | Ramesh Ramamoorthy |
| collection | DOAJ |
| description | Studying new chaotic flows with specific characteristics has been an open-ended field of exploring nonlinear dynamics. Investigation of chaotic flows is an area of research that has been taken into consideration for many years; thus, it helps in a better understanding of the chaotic systems. In this paper, an original chaotic 3D system, which has not been investigated yet, is presented in spherical coordinates. A unique feature of the proposed system is that its velocity becomes zero for a specific value of the radius variable. Hence, the system’s attractor is expected to be stuck on one side of a plane in spherical coordinates and inside or outside a sphere in the corresponding Cartesian coordinates. It means that the attractor cannot pass through the sphere or even touch it. The introduced system owns two unstable equilibria and a self-excited strange attractor. The 1D and 2D system’s bifurcation diagrams concerning the alteration of two bifurcation parameters are plotted to investigate the system’s dynamical properties. Moreover, the system’s Lyapunov exponents in the corresponding period of bifurcation parameters are calculated. Then, two 2D basins of attraction for two different third dimension values are explored. Based on the basin of attraction, it can be found that the sphere has attraction itself, partially, and some initial conditions are led to the sphere, not to the strange attractor. Ultimately, the connecting curves of the proposed system are explored to find an informative 1D set in addition to the system’s equilibria. |
| format | Article |
| id | doaj-art-c20d740c6ebd4d17b51c9f18250f3c9a |
| institution | DOAJ |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-c20d740c6ebd4d17b51c9f18250f3c9a2025-08-20T03:23:30ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/80687378068737A New Circumscribed Self-Excited Spherical Strange AttractorRamesh Ramamoorthy0Sajjad Shaukat Jamal1Iqtadar Hussain2Mahtab Mehrabbeik3Sajad Jafari4Karthikeyan Rajagopal5Center for Artificial Intelligence, Chennai Institute of Technology, Chennai, IndiaDepartment of Mathematics, College of Science, King Khalid University, Abha, Saudi ArabiaDepartment of Mathematics, Statistics and Physics, Qatar University, Doha 2713, QatarBiomedical Engineering Department, Amirkabir University of Technology, Tehran, IranBiomedical Engineering Department, Amirkabir University of Technology, Tehran, IranCenter for Nonlinear Systems, Chennai Institute of Technology, Chennai, IndiaStudying new chaotic flows with specific characteristics has been an open-ended field of exploring nonlinear dynamics. Investigation of chaotic flows is an area of research that has been taken into consideration for many years; thus, it helps in a better understanding of the chaotic systems. In this paper, an original chaotic 3D system, which has not been investigated yet, is presented in spherical coordinates. A unique feature of the proposed system is that its velocity becomes zero for a specific value of the radius variable. Hence, the system’s attractor is expected to be stuck on one side of a plane in spherical coordinates and inside or outside a sphere in the corresponding Cartesian coordinates. It means that the attractor cannot pass through the sphere or even touch it. The introduced system owns two unstable equilibria and a self-excited strange attractor. The 1D and 2D system’s bifurcation diagrams concerning the alteration of two bifurcation parameters are plotted to investigate the system’s dynamical properties. Moreover, the system’s Lyapunov exponents in the corresponding period of bifurcation parameters are calculated. Then, two 2D basins of attraction for two different third dimension values are explored. Based on the basin of attraction, it can be found that the sphere has attraction itself, partially, and some initial conditions are led to the sphere, not to the strange attractor. Ultimately, the connecting curves of the proposed system are explored to find an informative 1D set in addition to the system’s equilibria.http://dx.doi.org/10.1155/2021/8068737 |
| spellingShingle | Ramesh Ramamoorthy Sajjad Shaukat Jamal Iqtadar Hussain Mahtab Mehrabbeik Sajad Jafari Karthikeyan Rajagopal A New Circumscribed Self-Excited Spherical Strange Attractor Complexity |
| title | A New Circumscribed Self-Excited Spherical Strange Attractor |
| title_full | A New Circumscribed Self-Excited Spherical Strange Attractor |
| title_fullStr | A New Circumscribed Self-Excited Spherical Strange Attractor |
| title_full_unstemmed | A New Circumscribed Self-Excited Spherical Strange Attractor |
| title_short | A New Circumscribed Self-Excited Spherical Strange Attractor |
| title_sort | new circumscribed self excited spherical strange attractor |
| url | http://dx.doi.org/10.1155/2021/8068737 |
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