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Generation of hyperchaos from the Chen–Lee system via sinusoidal perturbation

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  • Tam, Lap Mou
  • Chen, Juhn Horng
  • Chen, Hsien Keng
  • Si Tou, Wai Meng

Abstract

A system with more than one positive Lyapunov exponent can be classified as a hyperchaotic system. In this study, a sinusoidal perturbation was designed for generating hyperchaos from the Chen–Lee chaotic system. The hyperchaos was identified by the existence of two positive Lyapunov exponents and bifurcation diagrams. The system is hyperchaotic in several different regions of the parameters c, ε, and ω. It was found that this method not only can enhance or suppress chaotic behavior, but also induces chaos in non-chaotic parameter ranges. In addition, two interesting dynamical behaviors, Hopf bifurcation and intermittency, were also found in this study.

Suggested Citation

  • Tam, Lap Mou & Chen, Juhn Horng & Chen, Hsien Keng & Si Tou, Wai Meng, 2008. "Generation of hyperchaos from the Chen–Lee system via sinusoidal perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 826-839.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:3:p:826-839
    DOI: 10.1016/j.chaos.2007.01.039
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    References listed on IDEAS

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    1. Chen, Hsien-Keng, 2005. "Synchronization of two different chaotic systems: a new system and each of the dynamical systems Lorenz, Chen and Lü," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1049-1056.
    2. Sheu, Long-Jye & Chen, Hsien-Keng & Chen, Juhn-Horng & Tam, Lap-Mou, 2007. "Chaos in a new system with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1203-1212.
    3. Park, Ju H., 2006. "Chaos synchronization between two different chaotic dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 549-554.
    4. Wu, Xiaoqun & Lu, Jun-an & Iu, Herbert H.C. & Wong, Siu-Chung, 2007. "Suppression and generation of chaos for a three-dimensional autonomous system using parametric perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 811-819.
    5. Chen, Hsien-Keng, 2005. "Global chaos synchronization of new chaotic systems via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1245-1251.
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    Cited by:

    1. Bouallegue, Kais & Chaari, Abdessattar & Toumi, Ahmed, 2011. "Multi-scroll and multi-wing chaotic attractor generated with Julia process fractal," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 79-85.
    2. Sheu, Long-Jye & Tam, Lap-Mou & Chen, Hsien-Keng & Lao, Seng-Kin, 2009. "Alternative implementation of the chaotic Chen–Lee system," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1923-1929.
    3. Karawanich, Khunanon & Prommee, Pipat, 2022. "High-complex chaotic system based on new nonlinear function and OTA-based circuit realization," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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