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Chaos Control and Synchronization in Fractional-Order Lorenz-Like System

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  • Sachin Bhalekar

Abstract

The present paper deals with fractional-order version of a dynamical system introduced by Chongxin et al. (2006). The chaotic behavior of the system is studied using analytic and numerical methods. The minimum effective dimension is identified for chaos to exist. The chaos in the proposed system is controlled using simple linear feedback controller. We design a controller to place the eigenvalues of the system Jacobian in a stable region. The effectiveness of the controller in eliminating the chaotic behavior from the state trajectories is also demonstrated using numerical simulations. Furthermore, we synchronize the system using nonlinear feedback.

Suggested Citation

  • Sachin Bhalekar, 2012. "Chaos Control and Synchronization in Fractional-Order Lorenz-Like System," International Journal of Differential Equations, Hindawi, vol. 2012, pages 1-16, August.
    • Handle: RePEc:hin:jnijde:623234
    DOI: 10.1155/2012/623234
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    Cited by:

    1. Laarem, Guessas, 2021. "A new 4-D hyper chaotic system generated from the 3-D Rösslor chaotic system, dynamical analysis, chaos stabilization via an optimized linear feedback control, it’s fractional order model and chaos sy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Mahmoudabadi, Parvin & Tavakoli-Kakhki, Mahsan, 2021. "Tracking control with disturbance rejection of nonlinear fractional order fuzzy systems: Modified repetitive control approach," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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