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Hyperchaos in a Conservative System with Nonhyperbolic Fixed Points

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Listed:
  • Aiguo Wu
  • Shijian Cang
  • Ruiye Zhang
  • Zenghui Wang
  • Zengqiang Chen

Abstract

Chaotic dynamics exists in many natural systems, such as weather and climate, and there are many applications in different disciplines. However, there are few research results about chaotic conservative systems especially the smooth hyperchaotic conservative system in both theory and application. This paper proposes a five-dimensional (5D) smooth autonomous hyperchaotic system with nonhyperbolic fixed points. Although the proposed system includes four linear terms and four quadratic terms, the new system shows complicated dynamics which has been proven by the theoretical analysis. Several notable properties related to conservative systems and the existence of perpetual points are investigated for the proposed system. Moreover, its conservative hyperchaotic behavior is illustrated by numerical techniques including phase portraits and Lyapunov exponents.

Suggested Citation

  • Aiguo Wu & Shijian Cang & Ruiye Zhang & Zenghui Wang & Zengqiang Chen, 2018. "Hyperchaos in a Conservative System with Nonhyperbolic Fixed Points," Complexity, Hindawi, vol. 2018, pages 1-8, April.
    • Handle: RePEc:hin:complx:9430637
    DOI: 10.1155/2018/9430637
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    References listed on IDEAS

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    4. Apostolos Argyris & Dimitris Syvridis & Laurent Larger & Valerio Annovazzi-Lodi & Pere Colet & Ingo Fischer & Jordi García-Ojalvo & Claudio R. Mirasso & Luis Pesquera & K. Alan Shore, 2005. "Chaos-based communications at high bit rates using commercial fibre-optic links," Nature, Nature, vol. 438(7066), pages 343-346, November.
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    Cited by:

    1. Zuo, Jiangang & Zhang, Jie & Wei, Xiaodong & Yang, Liu & Cheng, Nana & Lv, Jiliang, 2024. "Design and application of multisroll conservative chaotic system with no-equilibrium, dynamics analysis, circuit implementation," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    2. Yiming Wang & Fengjiao Gao & Mingqing Zhu, 2025. "Bidirectional Conservative–Dissipative Transitions in a Five-Dimensional Fractional Chaotic System," Mathematics, MDPI, vol. 13(15), pages 1-22, August.
    3. Dong, Qing & Zhou, Shihua & Zhang, Qiang & Kasabov, Nikola K., 2023. "A new five-dimensional non-Hamiltonian conservative hyperchaos system with multistability and transient properties," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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