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Dynamical Analysis of a 3-D Chaotic System with only Two Quadratic Nonlinearities

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Abstract

The paper reports the dynamical study of a three-dimensional quadratic autonomous chaotic system with only two quadratic nonlinearities, which is a special case of the so-called conjugate Lü system. Basic properties of this system are analyzed by means of Lyapunov exponent spectrum and bifurcation diagram. The analysis shows that the system has complex dynamics with some interesting characteristics in which there are several periodic regions, but each of them has quite different periodic orbits.

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References

  1. E. N. Lorenz, Deterministic nonperiodic flow, J. Atmos. Sci., 1963, 20(2): 130–141.

    Article  Google Scholar 

  2. D. Ruelle and F. Takens, On the nature of turbulence, Comm. Math. Phys., 1971, 20(3): 167–192.

    Article  Google Scholar 

  3. O. E. Rôsslor, An equation for continuous chaos, Phys. Lett. A, 1976, 57(5): 397–398.

    Article  Google Scholar 

  4. G. Chen and T. Ueta, Yet another chaotic attractor, Int. J. of Bifur. & Chaos, 1999, 9(7): 1465–1466.

    Article  Google Scholar 

  5. W. B. Liu and G. R. Chen, A new chaotic system and its generation, Int. J. of Bifur. & Chaos, 2003, 13(1): 261–267.

    Article  Google Scholar 

  6. S. J. Linz and J. C. Sprott, Elementary chaotic flow, Phys. Lett. A, 1999, 259(3): 240–245.

    Article  Google Scholar 

  7. J. H. Lü, G. Chen, D. Cheng, and S. Celikovsky, Bridge the gap between the Lorenz system and the Chen system, Int. J. of Bifur. & Chaos, 2002, 12(12): 2917–2926.

    Article  Google Scholar 

  8. Q. Yang, G. Chen, and T. Zhou, A unified Lorenz-type system and its canonical form, Int. J. of Bifur. & Chaos, 2006, 16(10): 2855–2871.

    Article  Google Scholar 

  9. T. Zhou and G. Chen, Classification of chaos in 3-D autonomous quadratic systems–I. Basic framework and methods, Int. J. of Bifur. & Chaos, 2006, 16(9): 2459–2479.

    Article  Google Scholar 

  10. Zeraoulia Elhadj and Hamri Nasr eddine, A generalized model of some Lorenz-type and quasi-attractors type strange attractors in three-dimensional dynamical systems, Int. J. Pure & Applied Mathematical Sciences, 2005, 2(1): 67–76.

    Google Scholar 

  11. Zeraoulia Elhadj, Analysis of a new chaotic system with three quadratic nonlinearities, Dynamics of Continuous, Discrete, and Impulsive Systems, 2007, 14b(4): 603–613.

    Google Scholar 

  12. S. J. Linz and J. C. Sprott, Elementary chaotic flow, Phys. Lett. A, 1999, 259(3–4): 240–245.

    Article  Google Scholar 

  13. G. Chen, Controlling Chaos and Bifurcations in Engineering Systems, CRC Press, Boca Raton, FL, 1999.

    Google Scholar 

  14. W. B. Liu and G. Chen, A new chaotic system and its generation, Int. J. of Bifur. & Chaos, 2003, 13(1): 659–661.

    Google Scholar 

  15. R. Genesio and A. Tesi, Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems, Automatica, 1992, 28(3): 531–548.

    Article  Google Scholar 

  16. A. M. Rucklidge, Chaos in models of double convection, J. Fluid. Mech., 1992, 237: 209–229.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Tébéssa, Tebessa, 12000, Algeria

    Zeraoulia Elhadj

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  1. Zeraoulia Elhadj
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Correspondence to Zeraoulia Elhadj.

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Elhadj, Z. Dynamical Analysis of a 3-D Chaotic System with only Two Quadratic Nonlinearities. J. Syst. Sci. Complex. 21, 67–75 (2008). https://doi.org/10.1007/s11424-008-9067-0

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  • DOI: https://doi.org/10.1007/s11424-008-9067-0

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