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3-scroll and 4-scroll chaotic attractors generated from a new 3-D quadratic autonomous system

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Abstract

This article introduces a new chaotic system of 3-D quadratic autonomous ordinary differential equations, which can display 2-scroll chaotic attractors. Some basic dynamical behaviors of the new 3-D system are investigated. Of particular interest is that the chaotic system can generate complex 3-scroll and 4-scroll chaotic attractors. Finally, bifurcation analysis shows that the system can display extremely rich dynamics. The obtained results clearly show that this is a new chaotic system which deserves further detailed investigation.

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References

  1. Chen, G., Dong, X. (eds.): From Chaos to Order: Methodologies, Perspectives and Applications. World Scientific, Singapore (1998)

    MATH  Google Scholar 

  2. Chen, G., Yu, X. (eds.): Chaos Control: Theory and Applications. Springer, Berlin (2003)

    MATH  Google Scholar 

  3. Lü, J., Lu, J., Chen, S. (eds.): Chaotic Time Series Analysis and Its Applications. Wuhan University Press, Wuhan (2002) (in Chinese)

    Google Scholar 

  4. Lü, J.H., Chen, G.R., Cheng, D.Z.: A new chaotic system and beyond: the generalized Lorenz-like system. Int. J. Bifurc. Chaos 14(5), 1507–1537 (2004). doi:10.1142/S021812740401014X

    Article  MATH  Google Scholar 

  5. Lü, J.H., Chen, G.R.: Generating multiscroll chaotic attractors: theories methods and applications. Int. J. Bifurc. Chaos 16(4), 775–858 (2006). doi:10.1142/S0218127406015179

    Article  MATH  Google Scholar 

  6. Chua, L.O. (ed.): CNN: A Paradigm for Complexity. World Scientific, Singapore (1998)

    MATH  Google Scholar 

  7. Chua, L.O., Komuro, M., Matsumoto, T.: The double scroll family. IEEE Trans. Circuits Syst. 33, 1072–1118 (1986). doi:10.1109/TCS.1986.1085869

    Article  MATH  MathSciNet  Google Scholar 

  8. Kennedy, M.P.: Three steps to chaos, part II: a Chua’s circuit primer. IEEE Trans. Circuits Syst.-I 40, 657–674 (1993)

    Article  MATH  Google Scholar 

  9. Qin, Q., Lin, W., Qiao, N.: Dynamical behaviours of Liu system with time delayed feedbacks. Chin. Phys. B 17(2), 569–572 (2008). doi:10.1088/1674-1056/17/2/035

    Article  Google Scholar 

  10. Qi, G.Y., Chen, G.R, van Wyk, M.A., van Wyk, B.J., Zhang, Y.H.: A four-wing chaotic attractor generated from a new 3-D quadratic autonomous system. Chaos Solitons Fractals 38(3), 705–721 (2008). doi:10.1016/j.chaos.2007.01.029

    Article  MATH  MathSciNet  Google Scholar 

  11. Sprott, J.C.: Simplest dissipative chaotic flow. Phys. Lett. A 228(4–5), 271–274 (1997). doi:10.1016/S0375-9601(97)00088-1

    Article  MATH  MathSciNet  Google Scholar 

  12. Lü, J.H., Chen, G.R.: A new chaotic attractor coined. Int. J. Bifurc. Chaos 12(3), 659–661 (2002)

    Article  MATH  Google Scholar 

  13. Li, T.C., Chen, G.R., Tang, Y., Yang, L.J.: Hopf bifurcation of the generalized Lorenz canonical form. Nonlinear Dyn. 47(4), 367–375 (2007). doi:10.1007/s11071-006-9036-x

    Article  MathSciNet  Google Scholar 

  14. Zhou, T.S., Chen, G.R., Celikovský, S.: Si’lnikov chaos in the generalized Lorenz canonical form of dynamical systems. Nonlinear Dyn. 39(4), 319–334 (2005). doi:10.1007/s11071-005-4195-8

    Article  MATH  Google Scholar 

  15. Wang, L., Ni, Q., Liu, P., Huang, Y.Y.: Chaos and its forming mechanism of a new Lorenz-like system. J. Dyn. Control 3, 1–6 (2005) (in Chinese)

    MATH  Google Scholar 

  16. Liu, W.B., Chen, G.R.: Can a three-dimensional smooth autonomous quadratic chaotic system generate a single four-scroll attractor? Int. J. Bifurc. Chaos 14(4), 1395–1403 (2004). doi:10.1142/S0218127404009880

    Article  MATH  Google Scholar 

  17. Li, D.Q.: A three-scroll chaotic attractor. Phys. Lett. A 372(4), 387–393 (2008)

    Article  MathSciNet  Google Scholar 

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Correspondence to L. Wang.

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Wang, L. 3-scroll and 4-scroll chaotic attractors generated from a new 3-D quadratic autonomous system. Nonlinear Dyn 56, 453–462 (2009). https://doi.org/10.1007/s11071-008-9417-4

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  • DOI: https://doi.org/10.1007/s11071-008-9417-4

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