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Study on the emergent mechanism of macroscopic dynamical structure in large dimensional dynamical systems

大维动力系统宏观动力结构涌现机制研究

基本信息

批准号：
13831007
负责人：
CHAWANYA Tsuyoshi
金额：
$ 2.24万
依托单位：
Osaka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2004
项目状态：
已结题

项目摘要

We studied on structures in phase space of large dimensional dynamical systems, that attract and hold trajectories for a considerable duration while they are not completely stable. Such structures are assumed to play an essential role in the emergence of slow dynamics with long tail in temporal correlation. We adopted globally coupled chaotic map systems as the main working model, and as a result of the research, we uncovered a type of psudo attractors in large dimensional chaotic systems, that can appear quite commonly and robustly. The psudo attractors of known types (especially in the dynamical systems with small number of degrees of freedom are basically remnant of attractor that collide with its basin boundary, and therefore observed only in quite limited area in parameter space, on the other hand, the newly uncovered ones can ovserved in broad area in the parameter space, since they are saddle set that are associated to the attractors in the dynamical system of continuous distribution, which corresponds to a limit of infinitely many degrees of freedom. The result obtained here would supply a basic idea to understand the behavior of the systems which is not completely disordered in spite of its essentially irreducible large number of degrees of freedom, a class of phenomena that are quite ubiquitous in so called complex systems. In addition to the above mentioned result, we found some novel phenomena in dynamical systems with small number of degrees of freedom, that are also related to slow dynamics like intermittency or itinerancy, and have a kind of robustness, and possibly be observed in the systems with a certain class of symmetry. The results show that there still much to explore in this area, the dynamics of complex systems, while they provide some clue to analyze quasi-stable states in such systems.

我们研究了大维动力系统相空间中的结构，这些结构在相当长的时间内吸引并保持轨道，而它们并不完全稳定。这种结构被认为在时间相关性中具有长尾的慢动力学的出现中起着至关重要的作用。我们采用全局耦合混沌映射系统作为主要的工作模型，通过研究发现了一类在高维混沌系统中普遍存在的具有鲁棒性的伪吸引子。已知类型的伪吸引子（特别是在自由度较少的动力系统中）基本上是与其盆边界碰撞的吸引子的残余，因此只能在参数空间中的相当有限的区域内观察到，而新发现的伪吸引子则可以在参数空间中的广阔区域内观察到，因为它们是与连续分布的动力系统中的吸引子相关联的鞍集，这对应于无限多个自由度的极限。这里得到的结果将提供一个基本的想法，以了解系统的行为，这是不完全无序的，尽管它本质上是不可约的大量的自由度，一类现象，是相当普遍的，在所谓的复杂系统。除了上述结果外，我们还发现了一些在小自由度动力系统中的新现象，这些现象也与慢动力学有关，如不稳定性或巡回性，并且具有某种鲁棒性，并且可能在具有某种对称性的系统中观察到。结果表明，在复杂系统动力学这一领域仍有许多研究工作要做，同时也为分析这类系统的准稳态提供了一些线索。