A study about complex motion caused by hierarchical structure and intermittency, in nonlinear dynamical system with large degree of freedom

大自由度非线性动力系统层次结构和间歇性引起的复杂运动研究

• 批准号: 12834012
• 负责人: HATA Hiroki
• 金额: $ 1.73万
• 依托单位: Kagoshima University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12834012/
• 关键词: high dimensional chaos; On-off intermittency; dynamical glass; chaotic itinerancy; anomalous diffusion; Hamilton chaos; generalized shift; volcano; カオス的遍歴現象; リアプノフ解析; フラクタル次元

Various hierarchical structures and motion hide in nonlinear dynamical systems, and so it is an important problem to build new methodology and general idea to understand it. We paid our attention to the hierarchical structure of invariant manifolds in nonlinear dynamical systems with the large degree of freedom as its approach, and understanding the motion theoretically and numerically is our aim of this research.( i ) To understand the complicated behavior of high dimensional chaos, we began studies invariant manifolds and On-off intermittency around them, already. We developed this study. Then we found that the complex behavior of the large degree of freedom chaos (chaotic itinerancy) is wondering motion between invariant manifolds and shown that we get clear characterization by statistical coarse-graining,( ii ) The properties of On-off intermittency that is the base of ( i ) had been argued with perturbation theory. We got new knowledge by treating them by non-preservative methods. … More ( iii ) Many non-chaotic attractors (fixed points, periodic orbits, and quasi-periodic orbits) can exist in a large degree of freedom (the number of attractor suddenly increases with increase of system size). We studied the properties from a viewpoint of response for noise in particular and was found that enough small noise tied attractor and caused intermittent phenomena. In addition, we found what we could describe the motion as anomalous diffusion in macro-quantities of system.( iv ) We studied also relation intermittency of chaos in conservative dynamical systems and low dimensional invariant structure.Next to a study about the behavior of dynamical systems mentioned above, we can develop approach for more complicated behavior. We started (a) a characterization of complicated behavior in generalized shift maps by anomalous diffusion, (b) an analysis of EEG pattern by time-series' entropy, (c) an analysis of intermittency of explosions of SAKURAJIMA volcano and (d) a study for the complicated behavior of dynamical systems with the hierarchical structure which seemed to have invariant manifold in an invariant manifold. Less

非线性动力系统中隐藏着各种各样的层次结构和运动，因此建立新的方法和总体思路来理解它是一个重要的问题。我们以大自由度的非线性动力系统中不变流形的层次结构为研究对象，从理论和数值上理解其运动是我们研究的目的。(I)为了了解高维混沌的复杂行为，我们已经开始研究不变流形及其周围的开关间歇现象。我们开展了这项研究。然后我们发现大自由度混沌(混沌巡游)的复杂行为是在不变流形之间的迂回运动，并表明我们通过统计粗粒化得到了明确的刻画。(Ii)用微扰理论论证了(1)开关间歇的性质，这是(I)的基础。我们通过对它们进行非防腐处理，获得了新的知识。…更多(Iii)许多非混沌吸引子(不动点、周期轨道和准周期轨道)可以在很大的自由度内存在(吸引子的数量随着系统规模的增加而突然增加)。我们特别从噪声响应的角度研究了它的性质，发现足够小的噪声束缚了吸引子，并导致了间歇现象。此外，我们还研究了保守动力系统中混沌的间歇性与低维不变结构之间的关系，进一步研究了上述动力学系统的行为，为研究更复杂的行为提供了方法。我们开始(A)用反常扩散刻画广义移位映射中的复杂行为，(B)用时间序列的熵分析脑电模式，(C)分析樱岛火山爆发的间歇性，以及(D)研究具有层级结构的动力系统的复杂行为，该系统似乎具有不变流形。较少

项目成果

Fujisaka,H. and Inoue,M.: "Characterization of Various Statistics of Diffusive Motion"Journal of Physical Society of Japan. 70. 2283-2286 (2000)

藤坂，H.

Y.Tsuda, S.Shirouzu, H.Isozaki, H.Sugano, M.Inoue: "Analysis of EEG pattern by time-series entropy"Clinical Neurophys isoloogy {\bf 111}, 2339. 111. 2339 (2000)

Y.Tsuda、S.Shirouzu、H.Isozaki、H.Sugano、M.Inoue：“通过时间序列熵分析 EEG 模式”临床神经生理学同源学 {f 111}, 2339. 111. 2339 (2000)

Nishi,Y., Setoyama,A. and Inoue,M.: "Nonperturbative Analysis of Chaos Synchronization in Coupled Logistic Map"Journal of Physical Society of Japan. 70. 3189-3192 (2000)

西，Y.，濑户山，A.

R.Ishizaki, H.Shiraishi, M.Kanie, M.Inoue: "Pathological Anomalous Diffusion Diffusion Generated by a Generalized Shift Map"Journal of Physical Society of Japan. 71(3月掲載予定). (2002)

R.Ishizaki、H.Shiraishi、M.Kanie、M.Inoue：“由广义位移图生成的病理异常扩散”《日本物理学会杂志》71（计划于 2002 年 3 月出版）。

Nishi,Y., Inoue,M., Tanaka,T. and Murai,M.: "Analysis of Time Sequences of Explosive Volcanic Eruptions of Sakurajima"Journal of Physical Society of Japan. 70. 1422-1428 (2000)

西 Y.、井上 M.、田中 T.