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Numerical Analysis, Circuit Simulation, and Control Synchronization of Fractional-Order Unified Chaotic System

Author

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  • Guohui Li

    (School of Electronic Engineering, Xi’an University of Posts and Telecommunications, Xi’an, Shaanxi 710121, China)

  • Xiangyu Zhang

    (School of Electronic Engineering, Xi’an University of Posts and Telecommunications, Xi’an, Shaanxi 710121, China)

  • Hong Yang

    (School of Electronic Engineering, Xi’an University of Posts and Telecommunications, Xi’an, Shaanxi 710121, China)

Abstract

The traditional method of solving fractional chaotic system has the problem of low precision and is computationally cumbersome. In this paper, different fractional-order calculus solutions, the Adams prediction–correction method, the Adomian decomposition method and the improved Adomian decomposition method, are applied to the numerical analysis of the fractional-order unified chaotic system. The result shows that different methods have higher precision, smaller computational complexity, and shorter running time, in which the improved Adomian decomposition method works best. Then, based on the fractional-order chaotic circuit design theory, the circuit diagram of fractional-order unified chaotic system is designed. The result shows that the circuit simulation diagram of fractional-order unified chaotic system is basically consistent with the phase space diagram obtained from the numerical solution of the system, which verifies the existence of the fractional-order unified chaotic system of 0.9-order. Finally, the active control method is used to control and synchronize in the fractional-order unified chaotic system, and the experiment result shows that the method can achieve synchronization in a shorter time and has a better control performance.

Suggested Citation

  • Guohui Li & Xiangyu Zhang & Hong Yang, 2019. "Numerical Analysis, Circuit Simulation, and Control Synchronization of Fractional-Order Unified Chaotic System," Mathematics, MDPI, vol. 7(11), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1077-:d:285077
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    References listed on IDEAS

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    2. Taiyong Li & Minggao Yang & Jiang Wu & Xin Jing, 2017. "A Novel Image Encryption Algorithm Based on a Fractional-Order Hyperchaotic System and DNA Computing," Complexity, Hindawi, vol. 2017, pages 1-13, November.
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