多种多翼吸引子共存的新型三维分数阶混沌系统  

A novel 3D fractional order chaotic system with coexistence of multiple types of multi-wing attractors

作　　者：徐昌彪[1,2] 何颖辉 吴霞 莫运辉 XU Changbiao;HE Yinghui;WU Xia;MO Yunhui(Schoot of Optoelectronia Engineering,Chongqing University of Posts and Telecommunications,Chongqing 400065,China;Schoot of Communication and Information Engineering,Chongqing University of Posts and Telecommunications,Chongqing 400065,China)

机构地区：[1]重庆邮电大学光电工程学院,重庆400065 [2]重庆邮电大学通信与信息工程学院,重庆400065

出　　处：《哈尔滨工业大学学报》2020年第5期92-98,共7页Journal of Harbin Institute of Technology

基　　金：教育部重点基金(02152)。

摘　　要：自然界的物理现象大多以分数阶的形式存在,整数阶微分方程正好是分数阶微分方程的特例.与整数阶模型相比,分数阶模型更接近真实的世界,具有更诱人的发展前景.为使分数阶混沌系统中共存的多翼混沌吸引子类型更加丰富,提出了一个新型三维分数阶混沌系统,此系统最大的特点是具有多种多翼混沌吸引子共存,即双翼、三翼和四翼混沌吸引子共存.通过相图、Lyapunov指数谱、分岔图等数值仿真,分析了系统的动力学特性,给出了其存在混沌吸引子的必要条件,即q>0.8224.固定参数,阶数q=0.98时,系统有双翼、双翼、四翼等混沌吸引子共存;q=0.83时,系统有双翼、三翼、四翼等混沌吸引子共存,表明了系统具有丰富的混沌特性.对系统进行了Multisim模拟电路仿真,仿真结果与数值分析相符,进一步验证了其混沌行为.采用分数阶Lyapunov稳定性理论以及定理1,设计了系统的自适应同步控制器,仿真表明响应系统与驱动系统在0.2s内达到同步,在0.2s内完成对未知参数的识别,因此,所设计的控制器是有效的.Most of the physical phenomena in the nature exist in the form of fractional order,and integer order equation is just a special case of fractional order equation.Compared with the integer order model,the fractional order model is closer to the real world and has a more attractive development prospect.In order to enrich the types of multi-wing chaotic attractors that coexist in fractional chaotic systems,a novel 3D fractional chaotic system is proposed in this paper.The most significant feature of the system is that there is a coexistence of muliple types of multi-wings chaotic attractors,namely the coexistence of two-wing,three-wing,and four-wing chaotic attractors.The dynamic characteristics of the system were analyzed via numerical simulations of phase diagram,Lyapunov exponent spectrum,and bifurcation diagram.A necessary condition for the existence of chaotic attractors was given,which is q>0.8224.For fixed system parameters,whenq=0.98,there is a coexistence of two-wing,two-wing,and four-wing chaotic attractors in the system;when q=0.83,there is a coexistence of two-wing,three-wing,and four-wing chaotic attractors,which indicates that the chaotic characteristics of the system are complex.The simulation results of an analog circuit of the system by the Multisim were consistent with those by the numerical analysis,which further venified the chaotic behaviors of the system.Based on the fractional Lyapunov stability theory and Theorem 1,an adaptive synchronous controller was designed.The simulation shows that the response system and the drive system reached the synchronization within the range of 0.2 s,and the identification of unknown parameters was completed within the range of 0.2 s,thus the controller is effective.

关 键 词：分数阶混沌系统 共存 多翼混沌吸引子 Multisim电路 自适应同步控制 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]