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,...

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Main Authors: Kadhim, Hayder Natiq, Banerjee, Santo, He, Shaobo, Md. Said, Mohamad Rushdan, Kilicman, Adem
Format: Article
Language:English
Published: Elsevier 2018
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
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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.
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institution Universiti Putra Malaysia
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language English
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publishDate 2018
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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