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Yan Wang, Shaobo He, Huihai Wang, Kehui Sun. BIFURCATIONS AND SYNCHRONIZATION OF THE FRACTIONAL-ORDER SIMPLIFIED LORENZ HYPERCHAOTIC SYSTEM[J]. Journal of Applied Analysis & Computation, 2015, 5(2): 210-219. doi: 10.11948/2015019
Citation: Yan Wang, Shaobo He, Huihai Wang, Kehui Sun. BIFURCATIONS AND SYNCHRONIZATION OF THE FRACTIONAL-ORDER SIMPLIFIED LORENZ HYPERCHAOTIC SYSTEM[J]. Journal of Applied Analysis & Computation, 2015, 5(2): 210-219. doi: 10.11948/2015019
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BIFURCATIONS AND SYNCHRONIZATION OF THE FRACTIONAL-ORDER SIMPLIFIED LORENZ HYPERCHAOTIC SYSTEM

  • 1 School of Physics Science and Technology, Xinjiang University, 830046, Urumqi, China;

  • 2 School of Physics and Electronics, Central South University, 410083, Changsha, China

  • Fund Project:
    Abstract
  • In this paper, dynamics of the fractional-order simplified Lorenz hyperchaotic system is investigated. Modified Adams-Bashforth-Moulton method is applied for numerical simulation. Chaotic regions and periodic windows are identified. Different types of motions are shown along the routes to chaos by means of phase portraits, bifurcation diagrams, and the largest Lyapunov exponent. The lowest fractional order to generate chaos is 3.8584. Synchronization between two fractional-order simplified Lorenz hyperchaotic systems is achieved by using active control method. The synchronization performances are studied by changing the fractional order, eigenvalues and eigenvalue standard deviation of the error system.
    MSC: 34C28;37N35
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    • References
  • [1] M. S. Abdelouahab, N. E. Hamri and J. W. Wang, Hopf bifurcation and chaos in fractional-order modified hybrid optical system, Nonlinear Dynamics, 69(2011), 275-284.

    Google Scholar

    [2] W. M. Ahmad and J. C. Sprott, Chaos in fractional-order autonomous nonlinear systems, Chaos, Solitons & Fractals, 16(2003), 339-351.

    Google Scholar

    [3] D. Y. Chen,R. F. Zhang and J. C. Sprott, Synchronization between integerorder chaotic systems and a class of fractional-order chaotic systems via sliding mode control, Chaos, 22(2012), 23130.

    Google Scholar

    [4] M. A. Ezzat, A. S. El Karamany and M. A. Fayik, Fractional order theory in thermoelastic solid with three-phase lag heat transfer, Archive of Applied Mechanics, 82(2012), 557-572.

    Google Scholar

    [5] J. W. Fan, N. Zhao and Y. Gao, Function synchronization of the fractionalorder chaotic system, Advanced Materials Research, 631(2013), 1220-1225.

    Google Scholar

    [6] C. Ionescu, J. T. Machado and D. R. Keyser, Fractional-order impulse response of the respiratory system, Mathematics with Applications, 62(2011), 845-854.

    Google Scholar

    [7] M. Javidi and N. Nyamoradi, Dynamic analysis of a fractional order phytoplankton model, Journal of Applied Analysis and Computation, 3(2013), 343-355.

    Google Scholar

    [8] E. Kaslik, S. Sivasundaram, Nonlinear dynamics and chaos in fractional-order neural networks, Neural Networks, 32(2011), 245-256.

    Google Scholar

    [9] S. Kuntanapreeda, Robust synchronization of fractional-order unified chaotic systems via linear control, Computers & Mathematics with Applications, 63(2012), 183-190.

    Google Scholar

    [10] E. T. McAdarns, A. Lackermeier and J. A. McLaughlin, The linear and nonlinear electrical properties of the electrode-electrolyte interface, Biosensors & Bioelectronics, 10(1995), 67-74.

    Google Scholar

    [11] A. G. Radwan, K. Moaddy and K. N. Salama, et al., Control and switching synchronization of fractional order chaotic systems using active control technique, Journal of Advanced Research, 5(2014), 125-132.

    Google Scholar

    [12] G. Q. Si, Z. Y. Sun and Y. B. Zhang, Projective synchronization of different fractional-order chaotic systems with non-identical orders, Nonlinear Analysis:Real World Applications, 13(2012), 1761-1771.

    Google Scholar

    [13] K. H. Sun, Y. Wang and X. Liu, Design and circuit implementation of hyperchaotic system based on linear feedback control, Journal of Circuits and Systems, 18(2013), 500-504(in Chinese).

    Google Scholar

    [14] H. H. Sun, A. A. Abdelwahab and B. Onaral, Linear approximation of transfer function with a pole of fractional power, IEEE Transactions on Automatic Control, 29(1984), 441-444.

    Google Scholar

    [15] V. E. Tarasov, Fractional integro-differential equations for electromagnetic waves in dielectric media, Theoretical and Mathematical Physics, 158(2009), 355-359.

    Google Scholar

    [16] Y. Xu, R. C. Gu and H. Q. Zhang, Chaos in diffusionless Lorenz system with a fractional order and its control, International Journal of Bifurcation and Chaos, 22(2011), 12500884.

    Google Scholar

    [17] R. Zhang and S. Yang, Adaptive synchronization of fractional-order chaotic systems via a single driving variable, Nonlinear Dynamics, 66(2011), 831-837.

    Google Scholar

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