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A hyperchaotic map with grid sinusoidal cavity

Author

Listed:
  • Yu, Mengyao
  • Sun, Kehui
  • Liu, Wenhao
  • He, Shaobo

Abstract

Based on closed-loop modulation coupling pattern and the model of sinusoidal cavity, a high-dimensional sinusoidal cavity hyperchaotic system is proposed. The number of sinusoidal cavities is controlled by the system parameters. By designing a piecewise-linear controller, the grid sinusoidal cavity attractors are obtained. The equilibrium points are theoretically analyzed through mathematical calculation. Taking the two-dimensional grid sinusoidal cavity hyperchaotic map as an example, dynamics of the system are analyzed by phase diagram, equilibrium points, Lyapunov exponents spectrum, bifurcation diagram, complexity and distribution characteristics. The results show that it has rich dynamical behaviors, including complicated phase space trajectory, hyperchaotic behavior, large maximum Lyapunov exponent and typical bifurcations. The proposed hyperchaotic map has advantages in complexity and distribution in the whole parameter space. Therefore, it has good application prospects in secure communication.

Suggested Citation

  • Yu, Mengyao & Sun, Kehui & Liu, Wenhao & He, Shaobo, 2018. "A hyperchaotic map with grid sinusoidal cavity," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 107-117.
    • Handle: RePEc:eee:chsofr:v:106:y:2018:i:c:p:107-117
    DOI: 10.1016/j.chaos.2017.11.004
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    References listed on IDEAS

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    1. Wang, Xingyuan & Wang, Mingjun, 2008. "A hyperchaos generated from Lorenz system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3751-3758.
    2. Zhang, Ying-Qian & Wang, Xing-Yuan, 2014. "Spatiotemporal chaos in mixed linear–nonlinear coupled logistic map lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 104-118.
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    Cited by:

    1. Zhu, Wanting & Sun, Kehui & He, Shaobo & Wang, Huihai & Liu, Wenhao, 2023. "A class of m-dimension grid multi-cavity hyperchaotic maps and its application," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Li, Chunbiao & Gu, Zhenyu & Liu, Zuohua & Jafari, Sajad & Kapitaniak, Tomasz, 2021. "Constructing chaotic repellors," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. Wang, Lingyu & Sun, Kehui & Peng, Yuexi & He, Shaobo, 2020. "Chaos and complexity in a fractional-order higher-dimensional multicavity chaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    4. Wu, Chenyang & Sun, Kehui, 2022. "Generation of multicavity maps with different behaviours and its DSP implementation," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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