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A universal method for constructing non-degenerate hyperchaotic systems with any desired number of positive Lyapunov exponents

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  • Fan, Chunlei
  • Ding, Qun

Abstract

Due to the limited machine word length of hardware devices, the dynamics of digital chaotic systems will degenerate. To combat this issue, we proposed a universal method that is based on singular value decomposition (SVD), which can reversely construct non-degenerate hyperchaotic systems with any desired number of positive Lyapunov exponents by controlling pre-specified singular values. To assess the practicability and effectiveness of the method, we construct a 6-dimensional non-degenerate hyperchaotic system as an example. Furthermore, based on the hyperchaotic system, a pseudorandom number generator (PRNG) with desirable statistical characteristics is designed for image encryption. Numerical simulations were performed to evaluate the security of the image encryption algorithm in terms of histogram, information entropy, differential attack test, etc. The proposed non-degenerate hyperchaotic system can be effectively applied in the field of multimedia data encryption and information security.

Suggested Citation

  • Fan, Chunlei & Ding, Qun, 2022. "A universal method for constructing non-degenerate hyperchaotic systems with any desired number of positive Lyapunov exponents," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005331
    DOI: 10.1016/j.chaos.2022.112323
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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.
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    Cited by:

    1. Surendar, R. & Muthtamilselvan, M. & Ahn, Kyubok, 2024. "Stochastic disturbance with finite-time chaos stabilization and synchronization for a fractional-order nonautonomous hybrid nonlinear complex system via a sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. Huiyan Zhong & Guodong Li & Xiangliang Xu & Xiaoming Song, 2022. "Image Encryption Algorithm Based on a Novel Wide-Range Discrete Hyperchaotic Map," Mathematics, MDPI, vol. 10(15), pages 1-23, July.
    3. Fan, Chunlei & Ding, Qun, 2023. "Constructing n-dimensional discrete non-degenerate hyperchaotic maps using QR decomposition," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    4. Ding, Dawei & Wang, Wei & Yang, Zongli & Hu, Yongbing & Wang, Jin & Wang, Mouyuan & Niu, Yan & Zhu, Haifei, 2023. "An n-dimensional modulo chaotic system with expected Lyapunov exponents and its application in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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