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A Fractional-Order System with Coexisting Chaotic Attractors and Control Chaos via a Single State Variable Linear Controller

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  • Ping Zhou
  • Meihua Ke
  • Peng Zhu

Abstract

A 3D fractional-order nonlinear system with coexisting chaotic attractors is proposed in this paper. The necessary condition of the existence chaos is . The fractional-order system exhibits chaotic attractors with the order as low as 2.5431. The largest Lyapunov exponent varying as fractional order is given. Furthermore, there are the coexisting “positive attractor†and “negative attractor†in this fractional-order chaotic system, and the necessary condition for “positive attractor†and “negative attractor†is obtained. Meanwhile, a control scheme for the stabilization of the unstable equilibrium is suggested via a single state variable linear controller. Numerical results show that the control scheme is valid.

Suggested Citation

  • Ping Zhou & Meihua Ke & Peng Zhu, 2018. "A Fractional-Order System with Coexisting Chaotic Attractors and Control Chaos via a Single State Variable Linear Controller," Complexity, Hindawi, vol. 2018, pages 1-7, June.
    • Handle: RePEc:hin:complx:4192824
    DOI: 10.1155/2018/4192824
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    References listed on IDEAS

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    1. Ping Zhou & Meihua Ke, 2017. "A New 3D Autonomous Continuous System with Two Isolated Chaotic Attractors and Its Topological Horseshoes," Complexity, Hindawi, vol. 2017, pages 1-7, November.
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    Cited by:

    1. Runzi Luo & Haipeng Su, 2018. "The Robust Control and Synchronization of a Class of Fractional-Order Chaotic Systems with External Disturbances via a Single Output," Complexity, Hindawi, vol. 2018, pages 1-8, November.

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