基于连续频段的杜芬方程一类混沌解的分析  

Analysis of a Type of Chaos Solution of Duffing Equations Based on Continuous Band

作　　者：李允公[1] 刘杰[1] 张金萍[2] 

机构地区：[1]东北大学机械工程与自动化学院,沈阳110004 [2]沈阳化工学院机械工程学院,沈阳110142

出　　处：《机械工程学报》2008年第1期81-86,共6页Journal of Mechanical Engineering

摘　　要：混沌信号的频谱中存在连续频段,这一特点通常归因于混沌的伪随机性,对连续频段的成因和特性却少有关注。基于两类杜芬方程,在其众多的解中发现一大类具有相同频域特征的混沌解,并对这类混沌解频谱中的连续频段的成因和特性进行研究。总结出连续频段在频域的位置和形状特征以及不同连续频段间的相互关系。针对连续频段,基于复解析小波对混沌解进行分析,发现混沌的调制特性和调制相似性,这两个特性有助于进一步揭示混沌解连续频段的成因以及同一混沌解不同连续频段间相似性的原因。进一步将混沌的调制特性和调制相似性与奇怪吸引子相结合,揭示奇怪吸引子的区域集中性和不同局部形状相似性。Continuous bands exsit in the spectrum of chaos signals because of the pseudorandomicity of chaos. But the cause and characteristics of continuous bands are neglected. Based on the solutions of two kinds of duffing equations, a large kind of chaos solution is found, which has the same characteristics in frequency domain, then the cause and characteristics of continuous bands are studied. The position and the shape characteristics of continuous bands are summarized, as well as the relations between different continuous bands. The analysis result of chaos solutions by complex analytical wavelet shows the modulation characteristic and modulation comparability of chaos, which redounds to reveal the cause of continuous bands for chaos solution and the cause of the comparability among different frequency bands for one chaos solution. Furthermore, the modulation characteristic and the modulation comparability are combined with the strange attractor to reveal the regional concentration and the similarity among shapes on different parts of the strange attractor.

关 键 词：混沌 幅值谱 连续频段 复解析小波 调制 奇怪吸引子 

分 类 号：O322[理学—一般力学与力学基础]