权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Study of Response, Propagation, and Reconstruction of High-dimensional Chaos with Coupled Maps

耦合映射高维混沌的响应、传播和重构研究

基本信息

批准号：
05836006
负责人：
KANEKO Kunihiko
金额：
$ 1.6万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1993
资助国家：
日本
起止时间：
1993 至 1994
项目状态：
已结题

项目摘要

We have studied features of high-dimensional chaos, including spatiotemporal chaos by means of coupled map lattices (CML). In particular we have clarified the following features.1.The pattern dynamics of the open-flow CML is studied. Spatial chaos with temporal periodicity is found, whose stability is analyzed by the co-moving Lyapunov exponents. Organization of periodic lattice of chaotic defects is found, whose mechanism is explained by the dynamical systems theory, while intermittent transition of such defects is found in stronger nonlinearity.2.Selection of attractors and amplified propagation of periodic inputs are studied in the open flow model. The study leads to the controalbility of patterns by tiny inputs. Possible applications to information processings are discussed.3.Two types of ordered states, clustered and dispersed states are found in Hamiltonian system with attractive and repulsive forces respectively. A variety of ordered states coexist depednding on initial conditions, which form onion structures in the phase space. This discovery gives a novel mechanism of order formation in many-particle systems.4.CML for Benard convection is analyzed, which reproduces all known phenomena in experiments and leads to several novel predictions on turbulent behaviors and chaotic itinerancy.5.The cascade information flow is found in globally coupled maps, while the chaotic itinerancy and dynamics of relationships between elements are studied in a variety of coupled map systems. Their relevenace to biological information prcoessings are discussed.

我们通过耦合图格（CML）研究了高维混沌的特征，包括时空混沌。具体明确了以下几个特点： 1.研究了开放流CML的模式动力学。发现了具有时间周期性的空间混沌，并通过共动李亚普诺夫指数分析了其稳定性。发现了混沌缺陷的周期晶格组织结构，其机理可以用动力系统理论来解释，并且在较强的非线性中发现了这种缺陷的间歇性转变。2.在开流模型中研究了吸引子的选择和周期输入的放大传播。该研究表明通过微小的输入即可控制模式。讨论了在信息处理中可能的应用。 3.哈密顿系统中存在两种有序态：簇态和分散态，分别具有吸引力和排斥力。根据初始条件，多种有序态共存，在相空间中形成洋葱结构。这一发现给出了多粒子系统中有序形成的新机制。4.分析了贝纳德对流的CML，它再现了实验中的所有已知现象，并导致了对湍流行为和混沌游动性的一些新颖预测。5.在全局耦合映射中发现了级联信息流，同时在各种耦合映射系统中研究了元素之间的混沌游动和关系动力学。讨论了它们与生物信息处理的相关性。