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Entropy 2019, 21(1), 27; https://doi.org/10.3390/e21010027

Parameter Identification of Fractional-Order Discrete Chaotic Systems

School of Physics and Electronics, Central South University, Changsha 410083, China
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Received: 17 December 2018 / Revised: 27 December 2018 / Accepted: 27 December 2018 / Published: 1 January 2019
(This article belongs to the Collection Wavelets, Fractals and Information Theory)
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Abstract

Research on fractional-order discrete chaotic systems has grown in recent years, and chaos synchronization of such systems is a new topic. To address the deficiencies of the extant chaos synchronization methods for fractional-order discrete chaotic systems, we proposed an improved particle swarm optimization algorithm for the parameter identification. Numerical simulations are carried out for the Hénon map, the Cat map, and their fractional-order form, as well as the fractional-order standard iterated map with hidden attractors. The problem of choosing the most appropriate sample size is discussed, and the parameter identification with noise interference is also considered. The experimental results demonstrate that the proposed algorithm has the best performance among the six existing algorithms and that it is effective even with random noise interference. In addition, using two samples offers the most efficient performance for the fractional-order discrete chaotic system, while the integer-order discrete chaotic system only needs one sample. View Full-Text
Keywords: parameter identification; particle swarm optimization; fractional difference; discrete chaotic system parameter identification; particle swarm optimization; fractional difference; discrete chaotic system
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Peng, Y.; Sun, K.; He, S.; Peng, D. Parameter Identification of Fractional-Order Discrete Chaotic Systems. Entropy 2019, 21, 27.

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