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，建立新的方法论和总体思想来理解它是一个重要的问题，本文以大自由度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本文的研究目标。（i）为了理解高维混沌的复杂行为，我们已经开始研究它们周围的不变流形和开关不变性。我们开展了这项研究。然后我们发现大自由度混沌的复杂行为（混沌巡游）是在不变流形之间的奇异运动，并通过统计粗粒化得到了清晰的刻画。（ii）利用微扰理论讨论了（i）的基础--开关不连续性的性质。通过非防腐处理，我们获得了新的认识。 ...更多信息 （iii）许多非混沌吸引子（不动点、周期轨道和准周期轨道）可以存在于大的自由度中（吸引子的数量随着系统大小的增加而突然增加）。我们研究的性质，特别是从响应的角度来看，噪声，发现足够小的噪声绑吸引子，并造成间歇现象。此外，我们还发现了可以用系统宏观量的反常扩散来描述这种运动的现象。（iv）我们还研究了保守动力系统中混沌的不变性与低维不变结构的关系，在研究上述动力系统行为的基础上，我们可以为更复杂的动力系统行为发展途径。（a）用反常扩散刻画广义移位映射的复杂行为，（B）用时间序列熵分析EEG模式，（c）分析SAKURAJIMA火山爆发的不稳定性，（d）研究具有不变流形中的不变流形的层次结构动力系统的复杂行为。少

项目成果

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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.