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A four-wing attractor and its analysis

Author

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  • Qi, Guoyuan
  • van Wyk, Barend Jacobus
  • van Wyk, Michaël Antonie

Abstract

In this paper, new properties of a four-dimensional chaotic system are investigated. These properties explain the behavior of the system and clarify why it can only generate two coexisting double-wing chaotic attractors but cannot produce a single four-wing chaotic attractor. It is shown that a new system with an extremely complex four-wing chaotic attractor and a larger positive Lyapunov exponent than the original system is formed by using these findings and introducing state feedback control to the system. Some basic dynamical behaviors and the complex structure of the new four-wing autonomous chaotic system are theoretically investigated. A detailed bifurcation analysis demonstrates the evolution process from local attractors to global attractors. The local attractors include two coexisting sinks, two coexisting single-wing periodic orbits and two coexisting double-wing chaotic attractors. The global attractors contain a diagonal double-wing periodic orbit, a diagonal double-wing chaotic attractor and a four-wing chaotic attractor. Spectral analysis indicates that the system in the four-wing chaotic mode has a very wide frequency bandwidth, confirming its random nature and its suitability to engineering applications such as secure communications.

Suggested Citation

  • Qi, Guoyuan & van Wyk, Barend Jacobus & van Wyk, Michaël Antonie, 2009. "A four-wing attractor and its analysis," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 2016-2030.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:4:p:2016-2030
    DOI: 10.1016/j.chaos.2007.09.095
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    References listed on IDEAS

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    1. Čelikovský, Sergej & Chen, Guanrong, 2005. "On the generalized Lorenz canonical form," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1271-1276.
    2. Li, Shujun & Álvarez, Gonzalo & Chen, Guanrong, 2005. "Breaking a chaos-based secure communication scheme designed by an improved modulation method," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 109-120.
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    Cited by:

    1. Doungmo Goufo, Emile Franc, 2017. "Solvability of chaotic fractional systems with 3D four-scroll attractors," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 443-451.
    2. Mathale, D. & Doungmo Goufo, Emile F. & Khumalo, M., 2020. "Coexistence of multi-scroll chaotic attractors for fractional systems with exponential law and non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).

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