分数阶四翼隐含吸引子混沌系统与电路设计  

Design of Chaotic System and Circuit with Fractional Four-wing Hidden Attractor

作　　者：林愿[1] 周细凤[1] 张向华[1] 龚军辉[1] 旷永红[1] LIN Yuan;ZHOU Xifeng;ZHANG Xianghua;GONG Junhui;KUANG Yonghong(College of Electrical and Information Engineering,Hunan Institute of Engineering,Xiangtan 411104,China)

机构地区：[1]湖南工程学院电气与信息工程学院,湘潭411104

出　　处：《湖南工程学院学报（自然科学版）》2022年第3期8-13,共6页Journal of Hunan Institute of Engineering(Natural Science Edition)

基　　金：湖南省自然科学基金资助项目(2019JJ60034);湖南省教育厅创新平台开放基金项目(20K036);湖南省教育厅科研资助项目(19C0474).

摘　　要：针对分数阶隐含吸引子的复杂拓扑结构,提出了一种新的分数阶混沌系统,该系统无平衡点,却可以显示四翼混沌吸引子.分析了该系统的动力学行为,由于该系统无平衡点,无法用Melnikov和Shilnikov等严格的数学方法来证明其混沌特性.本文通过数值仿真和电路实验来研究其混沌行为,数值仿真结果表明该分数阶系统能产生四翼混沌吸引子.并设计了p=0.9阶的电子电路进行电路实验,数值仿真与实验结果一致,均显示能产生拓扑结构复杂的四翼隐含吸引子.In response to the complex topological structure of the fractional order hidden attractor,a new fractional chaotic system is proposed in this paper,which has no equilibrium point but can display four-wing chaotic attractors.The dynamic behavior of the system is analyzed.Because the system has no equilibrium point,it is impossible to prove its chaotic characteristics with strict mathematical methods such as Melnikov and Shilnikov.This paper uses numerical simulation and circuit experiment to study its chaotic behavior.Numerical simulation results show that the fractional-order system can generate four-wing chaotic attractors.An electronic circuit with order p=0.9 is designed for circuit experiment.Numerical simulation and experimental results are consistent,and both show that it can produce a four-wing implicit attractor with a complex topology.

关 键 词：四翼 无平衡点 分数阶系统 隐藏吸引子 电路实现 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]