多混合阶混沌系统的特殊特性与同步

Special Characteristics and Synchronizations of Multi Hybrid-Order Chaotic Systems.

作者信息

Liu Jiaxun, Wang Zuoxun, Zhang Fangfang, Yin Yankai, Ma Fengying

机构信息

School of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China.

Shandong Computer Science Center (National Supercomputer Center in Jinan), Shandong Artificial Intelligence Institute, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250101, China.

出版信息

Entropy (Basel). 2020 Jun 16;22(6):664. doi: 10.3390/e22060664.

DOI:10.3390/e22060664

PMID:33286436

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7517199/

Abstract

Based on advantages of integer and fractional chaotic systems, hybrid chaotic systems and their definitions and some fundamental concepts are proposed, such as hybrid degree (HD), the lowest order (LO) and the total dimension order (TDO). The preliminary properties of hybrid Lorenz systems and hybrid forms of some classic chaotic systems are studied. Then, the relations between HD, LO and TDO with different parameters is investigated in chaotic systems. To be specific, HD is associated with fractional order. It is a directional method to search LO and TDO in chaotic systems. Finally, based on the incommensurate fractional stability theory, we accomplish combination synchronization for three different hybrid order chaotic systems. The simulation results verify the effectiveness of the synchronization controller.

摘要

基于整数和分数阶混沌系统的优势，提出了混合混沌系统及其定义和一些基本概念，如混合度（HD）、最低阶（LO）和总维数阶（TDO）。研究了混合洛伦兹系统的初步性质以及一些经典混沌系统的混合形式。然后，研究了混沌系统中HD、LO和TDO与不同参数之间的关系。具体而言，HD与分数阶相关。它是在混沌系统中搜索LO和TDO的一种定向方法。最后，基于非 commensurate 分数阶稳定性理论，实现了三个不同混合阶混沌系统的组合同步。仿真结果验证了同步控制器的有效性。