Parameter Identification of Fractional-Order Discrete Chaotic Systems

• Published in: Entropy (Basel, Switzerland) Vol. 21; no. 1; p. 27
• Main Authors: Peng, Yuexi, Sun, Kehui, He, Shaobo, Peng, Dong
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 01-01-2019; MDPI
• Subjects: Algorithms; Attractors (mathematics); Calculus; Chaos theory; discrete chaotic system; fractional difference; Interference; Optimization algorithms; Parameter identification; Particle swarm optimization; Random noise; Synchronism; Velocity; fractional difference; particle swarm optimization; discrete chaotic system; parameter identification
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e21010027

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.