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

School of Electronic Engineering, Xi’an University of Posts and Telecommunications, Xi’an, Shaanxi 710121, China
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Mathematics 2019, 7(11), 1077; https://doi.org/10.3390/math7111077
Received: 20 October 2019 / Revised: 3 November 2019 / Accepted: 5 November 2019 / Published: 8 November 2019
(This article belongs to the Section Engineering Mathematics)
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.
Keywords: fractional-order chaotic system; Adams prediction–correction method; Adomian decomposition method; fractional-order chaotic circuit; active control method fractional-order chaotic system; Adams prediction–correction method; Adomian decomposition method; fractional-order chaotic circuit; active control method
MDPI and ACS Style

Li, G.; Zhang, X.; Yang, H. Numerical Analysis, Circuit Simulation, and Control Synchronization of Fractional-Order Unified Chaotic System. Mathematics 2019, 7, 1077.

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