准周期激励Duffing系统中奇异非混沌吸引子的判别方法  

METHODS FOR DISCRIMINATION OF STRANGE NONCHAOTIC ATTRACTORS IN QUASI-PERIODICALLY DRIVEN DUFFING OSCILLATOR

作　　者：秦波 张颖 QIN Bo;ZHANG Ying(School of Mechanical Engineering,University of Shanghai for Science and Technology,Shanghai 200093,China;Department of Ultrasonic Intervention,Eastern Hepatobiliary Surgery Hospital,Naval Medical University,Shanghai 200438,China;School of Medicine,Tongji University,Shanghai 200092,China)

机构地区：[1]上海理工大学机械工程学院,上海200093 [2]海军军医大学第三附属医院(上海东方肝胆外科医院)超声介入科,上海200438 [3]同济大学医学院,上海200092

出　　处：《力学与实践》2024年第2期332-341,共10页Mechanics in Engineering

基　　金：研究生优秀学位论文培育基金项目(1021GK210006036-B20)资助。

摘　　要：奇异非混沌动力学是非线性动力学领域中的新课题。本文以准周期激励Duffing振子为例,对其产生的奇异非混沌吸引子(strange nonchaotic attractors,SNAs)进行分析。通过三维庞加莱截面和定量方法如傅里叶变换、李雅普诺夫指数、李雅普诺夫维数、关联维数和盒维数检测SNAs是否存在。研究结果表明,傅里叶变换无法判断混沌与奇异非混沌行为。而李雅普诺夫指数、李雅普诺夫维数可以作为检测系统混沌与非混沌指标。关联维数和盒维数显著表明系统奇异与非奇异性,从而阐明适用于准周期驱动Duffing振子中存在SNAs的判别方法,并为其他类似系统检测SNAs提供指导。Strange nonchaotic dynamics is a new topic in the field of nonlinear dynamics.In this work,we take the quasi-periodically driven Duffing oscillator as an example to analyze the generation of strange nonchaotic attractors(SNAs).The existence of SNAs is investigated using three-dimensional Poincarésections and quantitative methods such as Fourier transform,Lyapunov exponents,Lyapunov dimension,correlation dimension,and box dimension.The results indicate that Fourier transform is incapable of determining chaotic and strange nonchaotic behaviors.However,Lyapunov exponents and Lyapunov dimension can serve as indicators for detecting chaotic and nonchaotic behavior in the system.Correlation dimension and box dimension can clearly indicate the strangeness and nonstrangeness of the system,thus prove the existence of SNAs in the quasi-periodically driven Duffing oscillator and provide guidance for detecting SNAs in similar systems.

关 键 词：奇异非混沌吸引子 准周期激励 李雅普诺夫指数 关联维数 DUFFING振子 

分 类 号：O313[理学—一般力学与力学基础]