Complete synchronization of a novel 6-D hyperchaotic Lorenz system with known parameters

  • Authors

    • Ahmed S. Al-Obeidi University of Mosul
    • Saad Fawzi AL-Azzawi University of Mosul
    2019-03-28
    https://doi.org/10.14419/ijet.v7i4.18801
  • Chaos Synchronization, 6-D Hyperchaotic Lorenz Systems, Lyapunov Stability Theory.

  • Abstract

    There has been an increasing interest in field of high-dimensional systems and their synchronization phenomena. This paper deals with complete synchronization between two identical 6-D hyperchaotic Lorenz systems based on nonlinear control strategy. The designed control functions for the synchronization between the drive and response systems are succeed to achieve complete synchronization with the states of both systems are measurable and the parameters are known. Numerical simulations have verified the analytical synchronization technique.

     

     

     

  • References

    1. [1] S.F. AL-Azzawi and M.M. Aziz ,Strategies of linear feedback control and its classification, Telkomnika (Telecommunication, Computing, Electronics and Control) , Vol.17, No.4 (2019), In press; http://dx.doi.org/10.12928/telkomnika.v17i4.10989

      [2] S. Vaidyanathan, S. T. Kingni, A. Sambas, M. A. Mohamed and M. Mamat, "A New Chaotic Jerk System with Three Nonlinearities and Synchronization via Adaptive Backstepping Control", International Journal of Engineering & Technology. Vol.7, No.3, (2018), pp. 1936-1943.

      [3] HK. Chen, "Global Chaos synchronization of newchaotic systems via nonlinear control", Chaos, Solitons and Fractals, Vol.23, (2005) 1245-1251. https://doi.org/10.1016/S0960-0779(04)00373-X.

      [4] S.F. AL-Azzawi, "Stability and bifurcation of pan chaotic system by using Routh-Hurwitz and Gardan method", Appl. Math. Comput. Vol. 219, (2012), pp.1144-1152. https://doi.org/10.1016/j.amc.2012.07.022.

      [5] J. H. Park, "Chaos synchronization of a chaotic system via nonlinear control", Chaos Solitons Fractals, Vol. 25 (2005), 579-584. https://doi.org/10.1016/j.chaos.2004.11.038.

      [6] M. M. Aziz., S. F. AL-Azzawi, "Control and synchronization with known and unknown `parameters", Appl. Math., Vol.7 (2016), 292-303. https://doi.org/10.4236/am.2016.73026.

      [7] M. M. Aziz, S. F. AL-Azzawi, "Anti-synchronization of nonlinear dynamical systems based on Cardano’s method", Optik, Vol. 134, (2017), pp. 109–120. https://doi.org/10.1016/j.ijleo.2017.01.026.

      [8] M. M. Aziz, S. F. AL-Azzawi, "Hybrid chaos synchronization between two different hyperchaotic systems via two approaches", Optik, Vol.138, (2017), pp. 328–340. https://doi.org/10.1016/j.ijleo.2017.03.053.

      [9] M. M. Aziz., S. F. AL-Azzawi, "Chaos control and synchronization of a novel 5-D hyperchaotic Lorenz system via nonlinear control", Int. J. Mode. Phys. Appli., Vol. 2, (2015) 110-115.

      [10] Q. Jia, "Hyperchaos synchronization between two different hyperchaotic systems", Journal of Information and Computing. Science, Vol.3 (2008) 73–80.

      [11] D. Lu, A. Wang, X. Tian, "Control and synchronization of a new hyperchaotic system with unknown parameters", International Journal of Nonlinear Science. Vol.6 (2008) 224-229.

      [12] M.M. Aziz, S.F. AL-Azzawi, "Some Problems of feedback control strategies and its treatment", Journal of Mathematics Research; Vol. 9, No. 1; (2017) 39-49. https://doi.org/10.5539/jmr.v9n1p39.

      [13] Q. Yang,W. M. Osman and C. Chen., †A new 6D hyperchaotic

      system with four positive Lyapunov exponents coined.â€, Int. J. Bifurcation and Chaos. Vol.25, No.4, (2015), pp. 1550061–1550079. https://doi.org/10.1142/S0218127415500601.

      [14] S. A. Khan, Mixed Tracking and Projective Synchronization of 6D Hyperchaotic System Using Active Control, International Journal of Nonlinear Science, Vol.22, No.1 (2016), pp.44-53.

      [15] S.F. AL-Azzawi and M.M. Aziz.,†Chaos synchronization of nonlinear dynamical systems via a novel analytical approachâ€, Alexandria Engineering Journal, Vol.57, No.4, (2018), pp. 3493–3500. https://doi.org/10.1016/j.aej.2017.11.017.

  • Downloads

  • How to Cite

    S. Al-Obeidi, A., & Fawzi AL-Azzawi, S. (2019). Complete synchronization of a novel 6-D hyperchaotic Lorenz system with known parameters. International Journal of Engineering & Technology, 7(4), 5345-5349. https://doi.org/10.14419/ijet.v7i4.18801

    Received date: 2018-09-02

    Accepted date: 2019-01-14

    Published date: 2019-03-28