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Analysis of a new chaotic system

Profile image of Guoyuan QiGuoyuan Qi

2005, Physica A-statistical Mechanics and Its Applications

https://doi.org/10.1016/J.PHYSA.2004.12.040
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14 pages

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Abstract

This paper reports a new three-dimensional continuous quadratic autonomous chaotic system, modified from the Lorenz system, in which each equation contains a single quadratic cross-product term, which is different from the Lorenz, Ro¨ssler, Chen, Lu¨systems. Basic properties of the new system are analyzed by means of Lyapunov exponent spectrum and bifurcation diagrams. Analysis results show that this system has complex dynamics with some interesting characteristics. r

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References (12)

  1. C. Sparrow, The Lorenz Equations: Bifurcations Chaos and Strange Attractors, Springer, New York, 1982.
  2. O.E. Ro¨sslor, An equation for continuous chaos, Phys. Lett. A 57 (1976) 397-398.
  3. G. Chen, Controlling Chaos and Bifurcations in Engineering Systems, CRC Press, Boca Raton, FL, 1999.
  4. G. Chen, T. Ueta, Yet another chaotic attractor, Int. J. Bifurcat. Chaos 9 (1999) 1465-1466.
  5. T. Ueta, G. Chen, Bifurcation analysis of Chen's attractor, Int. J. Bifurcat. Chaos 10 (2000) 1917-1931.
  6. J.H. Lu¨, G. Chen, A new chaotic attractor coined, Int. J. Bifurcat. Chaos 12 (2002) 659-661.
  7. T.S. Zhou, G. Chen, Y. Tang, Chen's attractor exists, Int. J. Bifurcat. Chaos 14 (2004) 3167-3177.
  8. S. Ceˇlikovsky´, A. Vaneˇcˇek, Bilinear Systems and Chaos, Kybernetika 30 (1994) 403-424.
  9. J.H. Lu¨, G. Chen, D. Cheng, S. Celikovsky, Bridge the gap between the Lorenz system and the Chen system, Int. J. Bifurcat. Chaos 12 (12) (2002) 2917-2926.
  10. T.S. Zhou, G. Chen, Y. Tang, Complex dynamical behaviors of the chaotic Chen's system, Int. J. Bifurcat. Chaos 13 (9) (2003) 2561-2574.
  11. G. Chen, Chaotification via feedback: the discrete case, in: G. Chen, X. Yu (Eds.), Chaos Control, Springer, New York, 2003, pp. 159-178.
  12. X. Wang, Generating chaos in continuous-time systems, in: G. Chen, X. Yu (Eds.), Chaos Control, Springer, New York, 2003, pp. 179-204.

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