Hybrid synchronisation of vallis chaotic systems using nonlinear active control

  • Authors

    • Piyush Pratap Singh
    • Vikash Kumar
    • Eshan Tiwari
    • Vinay K. Chauhan
    2018-04-20
    https://doi.org/10.14419/ijet.v7i2.21.11834
  • Chaotic System, ENSO, hybrid synchronisation, lyapunov stability Theory, vallis System.

  • In this paper, hybrid synchronisation of Vallis chaotic systems using a nonlinear control technique is proposed. Vallis system represents the principal quantitative features of the El-Nino Southern Oscillation (ENSO) phenomenon. A nonlinear active control technique is used for hybrid synchronisation. Control laws are designed by using the sum of the relevant variables of the both mater and slave systems. Required Lyapunov stability condition is devised using Lyapunov stability theory. Numerical simulation results reflect the successful achievement of the proposed objectives. MATLAB is used for simulation.

     

     

  • References

    1. [1] Pecora LM & Carrol TL, “Synchronisation of chaotic systemsâ€, Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol.25, No.9, (2015).

      [2] Li C, Chen Q & Huang T, “Coexistence of anti-phase and complete synchronisation in coupled Chen system via single variableâ€, Chaos, Solitons and Fractals, Vol.38, (2008), pp.461-464.

      [3] Sudheer KS & Sabir M, “Hybrid synchronisation of hyperchaotic Chen systemâ€, National Conference on Nonlinear Systems Dynamics, Saha Institute of Nuclear Physics, (2009).

      [4] Sudheer KS & Sabir M, “Hybrid synchronisation of hyperchaotic Lu systemâ€, Pramana J. Phys., Vol.73, No.4, (2011), pp.781-786.

      [5] Sundarapandian V & Karthikeyan R, “Hybrid chaos synchronisation of hyperchaotic Lorenz and hyperchaotic Chen systems by active nonlinear controlâ€, Int. J. Electr. Power Eng., Vol.5, No.5, (2011), pp.186-192.

      [6] Sundarapandian V & Rasappan S, “Hybrid synchronisation of Arneodo and Rossler chaotic systems by active nonlinear controlâ€, LNICST, Vol.84, No.1, (2012), pp.73-82..

      [7] Vallis GK, “El Nino: a chaotic dynamical system?â€, Science, Vol. 232, (1986), pp.243-245.

      [8] Valli GK, “Conceptual models of El Nino and the Southern Oscillationâ€, J Geophys Res Oceans, Vol.93, No.11, (1988).

      [9] Samantaray J, Singh PP & Roy BK, “Anti-synchronisation of Vallis system using Sliding Mode Controlâ€, J. Control Instrumentation, Vol.5, No.3, (2014), pp.22-27.

      [10] Garay BM & Indig B, “Chaos in Vallis’ asymmetric Lorenz model for El Ninoâ€, Chaos, Solitons & Fractals, Vol.75, (2015), pp.253-262.

      [11] Slotine JE & Li W, Applied Nonlinear Control, New Jersey: Prentice Hall, (1991).

  • Downloads

  • How to Cite

    Pratap Singh, P., Kumar, V., Tiwari, E., & K. Chauhan, V. (2018). Hybrid synchronisation of vallis chaotic systems using nonlinear active control. International Journal of Engineering & Technology, 7(2.21), 50-52. https://doi.org/10.14419/ijet.v7i2.21.11834