Peng Yuexi, Sun Kehui, He Shaobo, Peng Dong
School of Physics and Electronics, Central South University, Changsha 410083, China.
Entropy (Basel). 2019 Jan 1;21(1):27. 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.
近年来，分数阶离散混沌系统的研究不断发展，此类系统的混沌同步是一个新课题。为解决现有分数阶离散混沌系统混沌同步方法的不足，我们提出了一种用于参数辨识的改进粒子群优化算法。针对Hénon映射、Cat映射及其分数阶形式，以及具有隐藏吸引子的分数阶标准迭代映射进行了数值模拟。讨论了选择最合适样本大小的问题，还考虑了噪声干扰下的参数辨识。实验结果表明，所提算法在六种现有算法中性能最佳，即使在随机噪声干扰下也有效。此外，对于分数阶离散混沌系统，使用两个样本可提供最有效的性能，而整数阶离散混沌系统仅需一个样本。
