Designing an M-dimensional nonlinear model for producing hyperchaos
This paper proposes an M-dimensional nonlinear hyperchaotic model (M-NHM) for producing new discrete-time systems with complex hyperchaotic behaviors. The M-NHM is constructed by designing an M-dimensional nonlinear system (M ≥ 2) to generate a chaotic behavior. To enhance the nonlinearity of M-NHM,...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2018
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| Online Access: | http://psasir.upm.edu.my/id/eprint/72199/ http://psasir.upm.edu.my/id/eprint/72199/1/Designing%20an%20M-dimensional%20.pdf |
| _version_ | 1848857063595180032 |
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| author | Kadhim, Hayder Natiq Banerjee, Santo He, Shaobo Md. Said, Mohamad Rushdan Kilicman, Adem |
| author_facet | Kadhim, Hayder Natiq Banerjee, Santo He, Shaobo Md. Said, Mohamad Rushdan Kilicman, Adem |
| author_sort | Kadhim, Hayder Natiq |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper proposes an M-dimensional nonlinear hyperchaotic model (M-NHM) for producing new discrete-time systems with complex hyperchaotic behaviors. The M-NHM is constructed by designing an M-dimensional nonlinear system (M ≥ 2) to generate a chaotic behavior. To enhance the nonlinearity of M-NHM, hence changing its behavior to hyperchaotic, an iterative chaotic map with infinite collapse (ICMIC) is composed. Mathematical analysis shows that the M-NHM has either no equilibria, or an arbitrarily large number of equilibria. Moreover, Routh−Hurwitz criterion reveals that all these equilibria are unstable when M ≥ 3. To investigate the dynamical properties and complexity of the M-NHM, we provide 2-NHM and 3-NHM as typical examples. Simulation results show that the 2-NHM and 3-NHM have good ergodicity, wide hyperchaotic behavior, highly sensitivity dependence, and high complexity. With all these features, the M-NHM would be an ideal model for secure communications and other engineering applications. |
| first_indexed | 2025-11-15T11:51:36Z |
| format | Article |
| id | upm-72199 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T11:51:36Z |
| publishDate | 2018 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-721992022-07-01T08:10:21Z http://psasir.upm.edu.my/id/eprint/72199/ Designing an M-dimensional nonlinear model for producing hyperchaos Kadhim, Hayder Natiq Banerjee, Santo He, Shaobo Md. Said, Mohamad Rushdan Kilicman, Adem This paper proposes an M-dimensional nonlinear hyperchaotic model (M-NHM) for producing new discrete-time systems with complex hyperchaotic behaviors. The M-NHM is constructed by designing an M-dimensional nonlinear system (M ≥ 2) to generate a chaotic behavior. To enhance the nonlinearity of M-NHM, hence changing its behavior to hyperchaotic, an iterative chaotic map with infinite collapse (ICMIC) is composed. Mathematical analysis shows that the M-NHM has either no equilibria, or an arbitrarily large number of equilibria. Moreover, Routh−Hurwitz criterion reveals that all these equilibria are unstable when M ≥ 3. To investigate the dynamical properties and complexity of the M-NHM, we provide 2-NHM and 3-NHM as typical examples. Simulation results show that the 2-NHM and 3-NHM have good ergodicity, wide hyperchaotic behavior, highly sensitivity dependence, and high complexity. With all these features, the M-NHM would be an ideal model for secure communications and other engineering applications. Elsevier 2018 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/72199/1/Designing%20an%20M-dimensional%20.pdf Kadhim, Hayder Natiq and Banerjee, Santo and He, Shaobo and Md. Said, Mohamad Rushdan and Kilicman, Adem (2018) Designing an M-dimensional nonlinear model for producing hyperchaos. Chaos, Solitons & Fractals, 114. 506 - 515. ISSN 0960-0779; ESSSN: 1873-2887 https://www.sciencedirect.com/science/article/pii/S0960077918307896 10.1016/j.chaos.2018.08.005 |
| spellingShingle | Kadhim, Hayder Natiq Banerjee, Santo He, Shaobo Md. Said, Mohamad Rushdan Kilicman, Adem Designing an M-dimensional nonlinear model for producing hyperchaos |
| title | Designing an M-dimensional nonlinear model for producing hyperchaos |
| title_full | Designing an M-dimensional nonlinear model for producing hyperchaos |
| title_fullStr | Designing an M-dimensional nonlinear model for producing hyperchaos |
| title_full_unstemmed | Designing an M-dimensional nonlinear model for producing hyperchaos |
| title_short | Designing an M-dimensional nonlinear model for producing hyperchaos |
| title_sort | designing an m-dimensional nonlinear model for producing hyperchaos |
| url | http://psasir.upm.edu.my/id/eprint/72199/ http://psasir.upm.edu.my/id/eprint/72199/ http://psasir.upm.edu.my/id/eprint/72199/ http://psasir.upm.edu.my/id/eprint/72199/1/Designing%20an%20M-dimensional%20.pdf |