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Designing an M-dimensional nonlinear model for producing hyperchaos


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


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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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
DOI Number: https://doi.org/10.1016/j.chaos.2018.08.005
Publisher: Elsevier
Keywords: High-dimensional systems; Hyperchaotic behavior; No equilibria; Stability; Complexity
Depositing User: Nurul Ainie Mokhtar
Date Deposited: 01 Jul 2022 08:10
Last Modified: 01 Jul 2022 08:10
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1016/j.chaos.2018.08.005
URI: http://psasir.upm.edu.my/id/eprint/72199
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