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Designing an M-dimensional nonlinear model for producing hyperchaos

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  • Natiq, Hayder
  • Banerjee, Santo
  • He, Shaobo
  • Said, M.R.M.
  • Kilicman, Adem

Abstract

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.

Suggested Citation

  • Natiq, Hayder & Banerjee, Santo & He, Shaobo & Said, M.R.M. & Kilicman, Adem, 2018. "Designing an M-dimensional nonlinear model for producing hyperchaos," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 506-515.
    • Handle: RePEc:eee:chsofr:v:114:y:2018:i:c:p:506-515
    DOI: 10.1016/j.chaos.2018.08.005
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    1. Mukherjee, Sayan & Palit, Sanjay Kumar & Banerjee, Santo & Ariffin, M.R.K. & Rondoni, Lamberto & Bhattacharya, D.K., 2015. "Can complexity decrease in congestive heart failure?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 439(C), pages 93-102.
    2. Costa, M. & Peng, C.-K. & L. Goldberger, Ary & Hausdorff, Jeffrey M., 2003. "Multiscale entropy analysis of human gait dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(1), pages 53-60.
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    1. Fan, Chunlei & Ding, Qun, 2023. "Constructing n-dimensional discrete non-degenerate hyperchaotic maps using QR decomposition," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Natiq, Hayder & Banerjee, Santo & Misra, A.P. & Said, M.R.M., 2019. "Degenerating the butterfly attractor in a plasma perturbation model using nonlinear controllers," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 58-68.

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