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On a four-dimensional chaotic system

Author

Listed:
  • Qi, Guoyuan
  • Du, Shengzhi
  • Chen, Guanrong
  • Chen, Zengqiang
  • yuan, Zhuzhi

Abstract

This paper reports a new four-dimensional continuous autonomous chaotic system, in which each equation in the system contains a 3-term cross product. Basic properties of the system are analyzed by means of Lyapunov exponents and bifurcation diagrams.

Suggested Citation

  • Qi, Guoyuan & Du, Shengzhi & Chen, Guanrong & Chen, Zengqiang & yuan, Zhuzhi, 2005. "On a four-dimensional chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1671-1682.
    • Handle: RePEc:eee:chsofr:v:23:y:2005:i:5:p:1671-1682
    DOI: 10.1016/j.chaos.2004.06.054
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    Citations

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    Cited by:

    1. Hammami, S. & Ben Saad, K. & Benrejeb, M., 2009. "On the synchronization of identical and non-identical 4-D chaotic systems using arrow form matrix," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 101-112.
    2. Li, Ruihong & Xu, Wei & Li, Shuang, 2009. "Anti-synchronization on autonomous and non-autonomous chaotic systems via adaptive feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1288-1296.
    3. Vincent, U.E., 2008. "Synchronization of identical and non-identical 4-D chaotic systems using active control," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1065-1075.
    4. Lei, Youming & Xu, Wei & Xie, Wenxian, 2007. "Synchronization of two chaotic four-dimensional systems using active control," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1823-1829.
    5. Barrio, Roberto, 2005. "Sensitivity tools vs. Poincaré sections," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 711-726.
    6. Wu, Wenjuan & Chen, Zengqiang & Yuan, Zhuzhi, 2009. "The evolution of a novel four-dimensional autonomous system: Among 3-torus, limit cycle, 2-torus, chaos and hyperchaos," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2340-2356.
    7. Lei, Youming & Xu, Wei & Shen, Jianwei, 2007. "Robust synchronization of chaotic non-autonomous systems using adaptive-feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 371-379.
    8. Zhou, Xiaobing & Wu, Yue & Li, Yi & Wei, Zhengxi, 2008. "Hopf bifurcation analysis of the Liu system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1385-1391.
    9. Du, Shengzhi & van Wyk, Barend J. & Qi, Guoyuan & Tu, Chunling, 2009. "Chaotic system synchronization with an unknown master model using a hybrid HOD active control approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1900-1913.
    10. Megam Ngouonkadi, E.B. & Fotsin, H.B. & Louodop Fotso, P. & Kamdoum Tamba, V. & Cerdeira, Hilda A., 2016. "Bifurcations and multistability in the extended Hindmarsh–Rose neuronal oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 151-163.
    11. Chen, Zengqiang & Yang, Yong & Yuan, Zhuzhi, 2008. "A single three-wing or four-wing chaotic attractor generated from a three-dimensional smooth quadratic autonomous system," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1187-1196.
    12. Ma, Junhai & Cui, Yaqiang & Liulixia,, 2009. "A study on the complexity of a business cycle model with great excitements in non-resonant condition," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2258-2267.
    13. Grassi, Giuseppe & Severance, Frank L. & Miller, Damon A., 2009. "Multi-wing hyperchaotic attractors from coupled Lorenz systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 284-291.

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