一类概周期驱动分段光滑系统的奇异非混沌吸引子特性分析  

Characteristic Analysis of Strange Nonchaotic Attractors for a Quasiperiodically-forced Piecewise Smooth System

作　　者：赵奕凡 沈云柱 杜传斌 ZHAO Yifan;SHEN Yunzhu;DU Chuanbin(School of Mathematics and Statistics,Qingdao University,Qingdao 266071,China;School of Mathematical Sciences,Jinan University,Jinan 250022,China)

机构地区：[1]青岛大学数学与统计学院,山东青岛266071 [2]济南大学数学科学学院,济南250022

出　　处：《复杂系统与复杂性科学》2024年第2期75-79,共5页Complex Systems and Complexity Science

基　　金：国家自然科学基金重点项目(11732014);山东省自然科学基金面上项目(ZR2021MA095)。

摘　　要：以一类概周期驱动分段光滑系统为研究对象,证实了奇异非混沌吸引子的存在性,并进一步分析了它的几种特性。首先采用相图和功率谱定性方法分析奇异非混沌吸引子的分形特性,再利用最大Lyapunov指数、相敏感指数、谱分布函数和有限时间Lyapunov指数分布定量方法进一步描述奇异非混沌吸引子的特性。结果表明,该系统在一定参数下存在奇异非混沌吸引子,该奇异非混沌吸引子表现出多种不同于其他类型吸引子的统计学特性。A quasiperiodically-forced piecewise smooth system is used as the research object to confirm the existence of strange nonchaotic attractors and further analyze several characteristics.Firstly,qualitative methods of phase diagram and power spectrum are used to analyze the fractal characteristics of strange nonchaotic attractors.Some quantitative methods such as the maximum Lyapunov exponent,phase sensitivity exponent,spectral distribution function and finite-time Lyapunov exponent are used to describe the characteristics of strange nonchaotic attractors.The results show that strange nonchaotic attractors can exist in the system under certain parameters,and exhibit a variety of statistical properties different from other types of attractors.

关 键 词：分段光滑系统 LYAPUNOV指数 相敏感指数 奇异非混沌吸引子 

分 类 号：O415.6[理学—理论物理] O415.5[理学—物理]