概周期驱动二维正弦系统的奇异非混沌吸引子特性分析  

Analysis of Strange Nonchaotic Attractors of Periodic Two-dimensional Sinusoidal Systems

作　　者：张玉玺 孙小淇 ZHANG Yuxi;SUN Xiaoqi(School of Mathematics and Statistics,Qingdao University,Qingdao 266071,China)

机构地区：[1]青岛大学数学与统计学院,山东青岛266071

出　　处：《复杂系统与复杂性科学》2024年第4期53-57,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：研究了一类概周期驱动二维正弦系统奇异非混沌吸引子的存在性与度量特性。首先通过相图描述了奇异非混沌吸引子的诞生过程,在给定参数下,奇异非混沌吸引子通过光滑环面倍化中断而出现分形现象;其次,通过最大李雅普诺夫指数和相敏感指数证实了该奇异非混沌吸引子;最后利用功率谱、有限李雅普诺夫指数分布和递归图表征了奇异非混沌吸引子特性。实验结果表明,系统中存在奇异非混沌吸引子,并且具有较好的统计学特性。The existence and metric characteristics of a class of quasiperiodic ally driven two-dimensional systems with sinusoidal functions are studied.Firstly,the birth process of strange nonchaotic attractors is described by phase diagram.Strange nonchaotic attractors are fractal due to the interruption of smooth torus doubling for the fixed parameters.Secondly,the strange nonchaotic attractors is confirmed by the largest Lyapunov exponents and phase sensitivity exponents.Finally,the power spectrum,finite Lyapunov exponents distribution and recurrence plots are used to characterize the strange nonchaotic attractors.According to the experimental results,there are strange nonchaotic attractors in the system and have good statistical characteristics.

关 键 词：奇异非混沌吸引子 相敏感指数 有限李雅普诺夫指数分布 

分 类 号：O415.6[理学—理论物理] N941.7[理学—物理]