物理学报2018，Vol.67Issue(5)：41-49,9.DOI:10.7498/aps.67.20172354
一种具有隐藏吸引子的分数阶混沌系统的动力学分析及有限时间同步
Dynamic analysis and finite time synchronization of a fractional-order chaotic system with hidden attractors
摘要
Abstract
Shilnikov criteria believe that the emergence of chaos requires at least one unstable equilibrium, and an attractor is associated with the unstable equilibrium. However, some special chaotic systems have been proposed recently, each of which has one stable equilibrium, or no equilibrium at all, or has a linear equilibrium (infinite equilibrium). These special dynamical systems can present chaotic characteristics, and the attractors in these chaotic systems are called hidden attractors due to the fact that the attraction basins of chaotic systems do not intersect with small neighborhoods of any equilibrium points. Since they were first found and reported in 2011, the dynamical systems with hidden attractors have attracted much attention. Additionally, the fractional-order system, which can give a clearer physical meaning and a more accurate description of the physical phenomenon, has been broadly investigated in recent years. Motivated by these two considerations, in this paper, we propose a fractional-order chaotic system with hidden attractors, and the finite time synchronization of the fractional-order chaotic systems is also studied. Most of the researches mainly focus on dynamic analysis and control of integer-order chaotic systems with hidden attractors. In this paper, based on the Sprott E system, a fractional-order chaotic system is constructed by adding an appropriate constant term. The fractional-order chaotic system has only one stable equilibrium point, but it can generate various hidden attractors. Basic dynamical characteristics of the system are analyzed carefully through phase diagram, Poincare mapping and power spectrum, and the results show that the fractional-order system can present obvious chaotic characteristics. Based on bifurcation diagram of system order, it can be found that the fractional-order system can have period attractors, doubling period attractors, and chaotic attractors with various orders. Additionally, a finite time synchronization of the fractional-order chaotic system with hidden attractors is realized based on the finite time stable theorem, and the proposed controller is robust and can guarantee fast convergence. Finally, numerical simulation is carried out and the results verify the effectiveness of the proposed controller. The fractional-order chaotic system with hidden attractors has more complex and richer dynamic characteristics than integer-order chaotic systems, and chaotic range of parameters is more flexible, meanwhile the dynamics is more sensitive to system parameters. Therefore, the fractional-order chaotic system with hidden attractors can provide more key parameters and present better performance for practical applications, such as secure communication and image encryption, and it deserves to be further investigated.关键词
隐藏吸引子/分数阶/混沌/有限时间同步Key words
hidden attractor/fractional order/chaos/finite-time synchronizing引用本文复制引用
郑广超,刘崇新,王琰..一种具有隐藏吸引子的分数阶混沌系统的动力学分析及有限时间同步[J].物理学报,2018,67(5):41-49,9.基金项目
国家自然科学基金创新研究群体科学基金(批准号:51521065)资助的课题.Project supported by the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (Grant No. 51521065). （批准号:51521065）
